Best Neighborhood/Area to Stay for 3 Nights in Belfast

Look into the Temple Bar area. It certainly fits your criterion of food / drinking / history. It tends to be one of the more expensive districts but there are good bargains. Its really the perfect place to stay: walking distance to both sides of the river and along the river to the Guinness brewery, near Trinity College and the Book of Kells for history, and only about 100 pubs within ten blocks.

Sorry, that note was for Dublin. I see your heading refers to Belfast.

That's okay, same question applies to Dublin, but I had heard about Temple Bar previously and concluded we would probably stay there for our Dublin portion of the trip. :)

We actually may only stay in Belfast for two nights...just trying to determine where we should stay there in relation to what is best to do/see as we don't know as much about Belfast.

We stayed in an apartment in the Titanic Quarter on our last trip and the location was excellent. The Titanic Museum is close by, and it's a short, scenic walk to get to Victoria Square and the attractions in the city...which is quite compact and pedestrian friendly. It was also nice to retreat to the relative quiet of the Quarter once we were done for the day. We peeked in on this place while we were there and it looked very nice: https://www.premierinn.com/gb/en/hotels/northern-ireland/antrim/belfast/belfast-titanic-quarter.html?INNID=BELTIT&ARRdd=04&ARRmm=02&ARRyyyy=2018&NIGHTS=1&ROOMS=1&ADULT1=2&CHILD1=0&COT1=0&INTTYP1=DB&SID=4&ISH=true&BRAND=PI&CID=GHF_US_mapresults_desktop_BELTIT
Regarding the Temple Bar area in Dublin: while it's certainly in the center of things it's also quite noisy into the wee hours. Unless you're really into crowds and noise I'd suggest looking a bit further away. Dublin is quite walkable too. We always stay in or near the Ballsbridge area - about a 20 minute walk from St. Stephens Green and Grafton St.

Emma,
What would you recommend beyond Temple Bar since we're talking about Dublin in here too? :)
We just want to be in walking distance to some cool things and have a good central location without having to rely on transportation the whole time. We are not afraid to walk a lot, so we'd be willing to walk 20-30 min to places (or more depending), but wouldn't want to be that far away from everything obviously.

I know the post was about Belfast, but it seems to have gone in a Dublin direction. I, too, would avoid saying right in Temple Bar. Very close and convenient, just across the river, is a cool hotel called The Morrison. If that's a bit over budget, have a look at Staunton's on the Green (right on Stephen's Green), or one of the O'Callahan's (Mont Clare is right in the heart of things, Davenport nearby.)

Another place that would work (within 20 min walk) is a simple guesthouse (with good breakfast) I stayed in recently with my high school aged daughter: Morehampton Townhouse. In a very nice part of town, 15-20 min walk to main sights.

Thank you everyone all these suggestions are much appreciated!

We are staying at the Premier Inn /Titanic Quarter mentioned above this upcoming August. We've stayed in this chain of hotels before and found them to provide a good value. The location in the Titanic Quarter was close to our top priority locations and I found that there is a bus from the train station that stops right outside the front door of the hotel. Our cost will be 73 pounds/night.