Hi MrsFogi
There are several city centre hotels in Belfast
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Europa Hotel - (used to hold title for most bombed hotel in the world or something like that) - its windows used to be continually boarded up
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Jury's (on the same street as Europa)
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Holiday Inn - has on site gym and pool
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McCausland's Hotel (nice boutique hotel in lovely building)
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Ten Square - expensive boutique hotel, seems to attract visiting pop stars eg. U2 etc
Restaurants - you could try Cayenne on Great Victoria Street, this restaurant belongs to Paul & Jeanne Rankin (celebrity TV chef - often appears on Ready Steady Cook) - food's quite nice and not too overpriced priced. He's also got a cheaper restaurant on the Malone Road called Raincity and various Rsocoff's cafes dotted throughout the city doing soups, sandwiches etc.
Or head into the not yet over-developed Cathedral Quarter for Nick's Warehouse in Hill Street (down a cobbled side street).
Or check out Deane's on Howard Street, which belongs to another celebrity chef, Michael Deane. He also has a fusion Thai place round the corner on Bedford Street called Chok Dee.
There's also a new-ish Japanese restaurant called Zen on Adelaide Street which has quite funky decor.
There're some nice little trendy bars around the city centre but they wouldn't really have a Irish flavour as such, would just be like trendy bars in most UK cities, Opium in the Cathedral Quarter, Apartment overlooking the City Hall, Bar Bacca just off Bedford Street.
For traditional bars, Pagan has recommended Crown which is lovely, or you could try the Duke of York which tucked down a side street in the Cathedral Quarter (claim to fame - Gerry Adams - him of Sinn Fein, apparently used to be a bartender there)
There's a Belfast Visitor Centre above Boots on Royal Avenue, the street facing the City Hall where you can pick up lots of leaflets for ideas of things to do in Belfast. The Black Taxi tours are quite interesting as they give you a little bit of insight into the "Troubles" and narrative is provided by your friendly Belfast taxi driver (complete with "hard man" accent!)
Enjoy yourselves!