I think that's right beisde the G-Mex so your best bet is to go downstairs when you get into manchester airport and get the train into Manchester Picadilly. Shouldn't be any more than £3 and cheaper than a taxi and you can comfortably walk to the hotel
Thereafter you've a fairly wide choice of pubs and clubs. If you're early to mid 20s then I suggest a trip to the print-works complex. It houses a great irish bar, the hard-rock cafe, several disco bar type places and opus night club which is open till all hours and well worth the visit. There's a few swanker places in Deansgate, which isn't far from there ( jump in a taxi and say "Deansgate", less than a fiver ). You may or may not want to avoid the canal though, it's a gay strip which we found out the hard way.
There's the arndale centre for a spot of shopping. My advice would be get the tram over to Salford from the Arndale or there abouts for the match. It leaves you in Old Trafford cricket ground, a stones throw from Old Trafford football ground and it's quicker and cheaper. Basically just follow the crowd. Likewise, the tram back is pretty handy. Around Salford before the match, The Bishops Bliaze is a great little pub for atmosphere or if you want to venture further there's a few less packed pubs in the Salford Quays.
Manchester is a great ould town, you shouldn't have to try too hard to have a decent time.