The Lacemarket is the old lace factory buildings and runs into area known as Hockley. If you're asking directions, ask for Hockley as it's the busiest area and just up from the Market Square. It's a great option for a one night stay. Full of bars, cafes, restaurants and home to the Broadway cinema, which shows both indie and quality mainstream films and also its own bar and cafe. Great atmosphere in that area, do not miss it to go to Cineworld or the Cornerhouse (they could be anywhere. ...you want to experience Nottingham!). Broadway tickets also cheaper than the national chains, it's a win-win.
Ibis hotel is 1-2 min walk away ftom Hockley area and about 5-8 mins walk from the train station or it has a tram stop outside.
For food, I've heard good things about 'Sexy Moma Loves Spaghetti ' and Edin's (same ownership). Think there are two of each now. All in the Hockley area and a couple opposite Broadway. There"s also 'Oscar and Rosie's (near The Angel pub) for fantastic pizza....very slightly more £ than Pizza Express but worth it. Annie's is famous for huge burgers, but I"ve only ever been once and that was enough for me...depends how burger-mad you are! Lots of Vietnamese, Chinese, Thai and Indian choices near Broadway too.
Craft beer...... Google "Castle Rock Brewery' They brew in the city, down by the railway station but have pubs or micropubs scattered all over the city.
For Saturday Night/Sunday Morning (another great Nottingham reference), there's the Contemporary art gallery. Usually one or two exhibitions, fab gift shop and cafe. Or, Google 'Sneinton Market'. This is just over the road from the Hockley area and has lots of tiny independent shop and makers units, the Fox and Grapes pub serving Castle Rock beer, and on some nights is alive with open air events and live music (only sometimes though, so Google first).
Can only scratch the surface here....a great city that gets into your soul....hope you have a fab time and get to return for a longer stay.