Well, if you're staying near The Royal Exchange Theatre then you're right in the heart of Manchester! Good area with everything you could want right on your doorstep!
Manchester is quite compact. You won't be far from the 'attractions'. But there are some other things that you can do as well...
My top few ideas... see if there is a band playing nearby that you'd like to see. Several great venues (The Ritz, Albert Hall, The Academy venues, The Deaf Institute, Band On The Wall...) Manchester crowds are always well up for it!
If you're interested in Manchester and its history, take a walking tour. Several are available, Google it!
Consider a half day or full day at Salford quays, a few miles away, easily accesible by tram. The Lowry Gallery, Imperial War Museum North, a tour of the BBC studios (only available on certain days)...
If you are into beautiful old buildings, then The John Rylands Library is certainly worth a look.
If you're in Manchester for four days, why not a train trip to a nearby city? Liverpool is great and not so far away. Chester is also worth a look if you like ancient history.
And there are many fine pubs in Manchester...
As for a potential NMA-pals meet in Manchester, post a thread, not sure if I can make it (financial bad times...

) but hey, put it out there, I'll do my best to make it, I know some damn fine places to drink in lovely Manchester!
Feel free to get back to me if you want any elaboration as to any of the things I mentioned...
