A good source for sussing out places to eat in Ireland is the Bridgestone Guides (here is the link for Limerick: http://www.bestofbridgestone.com/taxo...). There are Bridgestone shields on the doorways of establishments that have been given this award. Limerick is within easy access of fishing ports, so fresh seafood is certainly a possibility. If you have kitchen facilities, you can find seafood, local produce, and cheese at the Milk Market on Saturdays in downtown Limerick.
Mostly what you can get in Ireland is pub grub (which can be very good as well as affordable; there is often much debate on the best source of fish & chips). You can count on good lamb and pork (beef not so much as most of the agricultural land is too poor for cattle) and fabulous cheese. There are around 200 artisanal cheese makers in the Republic of Ireland, most of which are in County Cork (the next county east of Limerick). Most varieties of potatoes here are not represented in the states If you want an outing, go to the Irish Seed Savers facility in Scarriff.
Also available in Ireland are holdovers from once being under the thumb of the British Empire. There are Irish versions of certain British comfort foods (e.g. Kerry Pie for Cornish Pastys), as well as imports from former British Colonies (i.e., good Indian food). You can also find cuisine from neighboring European countries, predominantly French.
So far, my favorite restaurant in Limerick is "Copper & Spice" (2 locations). The prices are reasonable, the ingredients are fresh, and the mixture of flavors are nice. I have been to "The French Table" but was not impressed.
This season is entering into "the hungry gap" (the root vegetables are running low and the spring vegetables have yet to arrive). January is mostly root veg and winter squash. Farmer's with polytunnels can be producing rocket (arugula) and other leafy greens including different varieties of kale.
If you venture further afield, the Dingle peninsula (An Daingean) is gorgeous, and this time of year it is not full of tourists. Fresh seafood should be even easier to come by (not to miss: smoked wild irish salmon, moules frites, and squid).
Hope this helps.