Takashi in Wicker Park sounds right up your alley-- beautiful, delicious, Michelin-starred French-American with a Japanese touch. Definitely doable for under 100 a person, plenty of tables open right now, and very easy to get to.

You can leave your name and #, then go; no need to stick around or check back. In addition, bar seats are all first come, first serve, so you may even get a spot when you first come in. I have never had to wait as long as they actually quote me; so many people attrit off the list.

While you wait, you may want to get a drink nearby. Across the street (first floor of your hotel, actually) is a nice wine bar called Eno. Just a few blocks west on illinois is a bar/restaurant called Sable that has quite a nice cocktail menu, and about the same distance away, at Ohio+state, is a place called Watershed-- it's my favorite hidden gem in that area. It's in the basement of a silly, posh-looking champagne bar called "Pops", but don't be fooled! You go to the basement, where you will find interesting beers, wonderful drinks, and a quiet, laid-back atmosphere. The food is also quite tasty, if you get peckish while waiting for PP.

Owine & Engine and West Town Tavern come to mind, as places that serve wonderful meat and potatoes (have you had the owine and engine steaks?!). They both take reservations, and neither one is rowdy. (That said, last time they were here, I took my 87 year old Midwestern, meat-and-potatoes grandpa and grandma to Longman & Eagle, where they had the time of their lives-- first time doing shared plates, first time having all these new-fangled foods; they still talk about it!)

I would say Z&H sandwiches on 57th st is the tastiest spot nearby, and it's open Sundays. They have excellent breakfast and lunch sandwiches, good coffee, outdoor seating on the sidewalk or a back patio. Tasty prosciutto and jamon serano, good croissant sandwiches, a great goat cheese and raisin veg sandwich , etc. They also serve soups and other specials. A cute, hip cafe, and just around the corner from Robie.

I have been to El, but not Schwa; El was a special dining experience, but to use your words, it was not a a blast-- and it was not as memorable as other meals I've had at similar venues, eg Bonsoiree.

There are some fantastic gastropub type places in Chicago; casual vibe but delicious dishes, mainly shared plates. In that genre, I would recommend purple pig, the publican, longman and eagle, owen and engine.
For a casual lunch and a vibrant atmosphere, big star tacos is a lot of fun. It is in a neighborhood called wicker park, which is a fun area for walking, shopping, eating , drinking. In the same part of the city, there is also a bar called Map Room-- awesome beer list.

Never been to RPM, and I only went to Quartino's once. I don't really remember the meal, sorry!

To round out your weekend, here are some nearby spots for drinks:
Sable Bar and Kitchen: they have an excellent and *extensive* cocktail menu. NoMI at the Park Hyatt has a lovely terrace overlooking the city, and tasty summer drinks. Gilt Bar has great drinks.

A new Italian joint that's garnering praise:
http://balenachicago.com/
Balena

If you would also like to check out other neighborhoods, there are some great sunday brunch/lunch options in Bucktown/Wicker Park. Takashi has a fantastic noodle lunch on Sundays, and The Bristol does a mean brunch. You can stroll around the neighborhood after; boutiques, coffee shops, vintage, etc.

1) Ditch the other couple :)
2) Purple Pig is wonderful. I have not been to the Gage, but by other's accounts it is nowhere near as interesting as Purple Pig. Arrive early at PP, or go late.
3) If you're willing to take a short cab ride to the West Loop, you might enjoy The Publican; scrumptious plates for sharing, a great Sunday brunch, and unlike PP, they take reservations.
4) Places like publican and purple pig do, indeed, have steak and potatoes, and believe me, the steaks and potatoes will be good. I;ve taken my small-town wisconsin meat and potatoes relatives to PP, Longman & Eagle, and Publican, and trust me, everyone went home happy. Who doesn't love to die for sausages, roasted pork shoulder and mashed potatoes, etc.

Don't know if it's too late, but Nomi is right off of Michigan Ave; lovely terrace, was there tonight and it was under 50 with a cocktail each, tax, and tip.

A short cab ride away in the west loop, you'll find tons of options: Avec (no res, casual but chic, tasty and extremely reasonable prices), Maude's Liquor Bar, the Publican (delicious small plates), Au Cheval (a hip little 'upscale diner' deal), Vera (wine bar and refined tapas); all are in your price range.

Two blocks south on Randolph, things will be more lively. Many bars. I've done the Publican-then-Aviary combo, and spent the in-between time strolling around Randolph. There is an upscale diner called Au Cheval 2 mins from Publican, where you can get a drink and a mean root beer float. There is a Starbucks, if you just want to chill and get coffee, and there is a Billiards place 2 blocks south of Aviary (I know about it because the Aviary doorman mentioned it! He said it was kinda divey, but still something quirky and fun to do while waiting).

Longman & Eagle does a great brunch.

Have you thought about Blackbird for lunch? It's to the west of the river, but for $22 the three course lunch is an amazing weekday option, and worth the walk/short cab ride!

The Longman brunch is great. If you've never been, go! I like the duck confit hash, the fried chicken waffles, and the wild boar sloppy joe. They have tasty Bloody Marys.

Purple Pig is also awesome. Do not let the name fool you. Their non-pork offerings are extensive, and delish. I take vegetarian friends there-- between the burrata, crispy brussel sprouts, salads, eggplant caponata, mushrooms, etc, you can have quite the feast without any flesh at all.

Longman & Eagle and Cafe Lula are right around the corner form Yusho, and I like them much better; but they don't take reservations.

Yusho was ok; there were a few delicious bites, but some of the portion sizes were small, or awkward to share. The fried chicken they served us was literally raw. They were mortified, and tried to make it right, but it was a pretty unappetizing blunder.

If you're going for the casual small plates thing, and require reservations, then Publican is also delicious, and despite the seeming porkiness of the place, their mussels, fish, oysters, chicken, vegetables, and desserts make for scrumptious dining. The Aviary is right down the street, so after you're done eating, you can head over there for some whimsical and weird cocktails.

I think purple pig and longman & eagle both fit he bill-- fun, delicious, porky, shared plates. Neither one takes reservations, but I have dined at both with groups of 6 and 7; just need to get there early or plan to grab a drink nearby while waiting.

You might also look into telegraph, yusho (Japanese street food/ small plates), cafe lula.

Fyi: They are byob, but just got a liquor license and serve wine flights. Saturdays they do a special tasting menu--you have to call to book, it fills up fast-- and Sundays they do either 4 or 7 course "chef's whim" menu.

El is great; I will add Bonsoiree as another fantastic choice; intimate, byob, superb food.

Also, I hear the private tatami rooms at L20 are awesome.

10 course cocktail tasting menu at the Aviary? You're right up close, watching the kitchen wizardry.

Or EL...essentially, everyone is at the chef's table! It's like an intimate dinner party; you can even wander around the kitchen, ask questions, and help serve, if you like. http://elideas.com/

Went to Boka on friday-- the restaurant week menu was weak. We tried all three entrees; all well cooked, but nothing special. The gnocchi+mushrooms were solid, the fish was nice, but none of us cared for the chicken dish.

The best dishes we had were the desserts, which we subbed in from the regular menu :). They were divine...but again, they were off the regular menu. Just go back for the real deal some other week, I say!

I second Bonsoiree...it is intimate, chic, casual, and delicious. It's BYOB, but they just got a liquor licence and serve wine pairings, which might be convenient if you are traveling.

As the others mentioned, Purple Pig is close to you and awesome, but the wait can be long; one strategy is to put your name down early (early, I tell you!), then grab a glass or two of wine across the street at Eno, the wine bar in the Intercontinental Hotel building.

Places nearby that take reservations: GT Fish & Oyster, Sable, Nomi, Maud's Liquor Bar, Blackbird, Naha
A few more places that don't: Vera, Avec