I've name changed for this, to an appropriately Limerick themed one in honour of the Rubber Bandits 
I live about 20 minutes from Limerick and know the city & the area reasonably well.
OP, if your DH is going to be based at UL you should look at living in the Castletroy or Monaleen areas as they are very close to the university. It's a nice area of the city and close to shops, schools etc. There's a good secondary school, Castletroy College, and several primary schools with good reputations close by. The university itself is good.
Adare is lovely, but it's very touristy & it's the wrong side of the city for the university and traffic can be busy. The N7 motorway has improved transport links in recent years so getting from one side of the city to the other is a lot easier than it was, but there is still rush hour congestion as in every city.
Killaloe/Ballina is a lovely twin village on either side of the river Shannon, linked by a bridge. It's very popular with people working in UL and is only 20 minutes away. Someone said upthread it's the home of a lot of the Munster rugby players - it certainly was a few years ago but the only ones I know living there now are retired. It's quite cosmopolitan for a smallish Irish village, during the Celtic Tiger years the local primary school had children of 14 nationalities and 9 different religions. There's a small secondary school in the village which has a socially mixed intake and a reasonable reputation locally, and good local shops & services.
Castleconnell is another pretty village which is even closer to UL.
Limerick has changed a lot in recent years, there's been a great deal of investment to improve the city centre and there's a decent range of shops. Still no Marks & Spencers though, sadly.
The 'stab city' nickname isn't relevant any more as Limerick has cleaned up its act a lot. Yes there are a few dodgy areas, but every city has those. You soon learn where to avoid. The city centre is safe during the day and the usual precautions need to be taken at night. I've always found it a friendly enough place, and I'm a blow in. I've never felt in the least bit threatened.
The weather isn't the best, but it tends to be damp rather than cold. I don't mind it. I've always said you don't come to live in Ireland for the weather! In Limerick you're only an hour's drive from a beach if you do get some decent sunshine.
OP, if you'd like any more info, feel free to PM me.