My favourite bar is WhistleBinkies, just off the Royal Mile - small door off of South Bridge, or main entrance on Niddry Street. It's got live music til 3am every day - can get a bit busy, but you should be ok this time of year. The other bars on the Royal Mile are ok, in general the further away from the castle the more authentic the atmosphere. Unfortunately, as Stan mentioned, all the real pubs have been closed down - even the Volunteer Arms immortlised by Irvine Welsh!
Steer clear of the Grassmarket, it's become very tacky and is full of hen and stag parties (don't think there's any rugby on this weekend, as that's also where the egg-chasers normally end up). If you do end up there, the Beehive is probably the better of a bad bunch.
Plenty of boozers up on Rose Street too, just behind all the shops on Princes Street - leave the women to browse whilst you have a drink! There's an excellent Tapas restaurant El Paso Tapas Bar on Dundas Street not far from there.
Go to the Camera Obscura up by the castle - I loved it. It's like a funky art gallery, a world of illusions which is good for a laugh, especially if you've had a couple of drinks - the turning tunnel is a hoot....The Whiskey Museum is on the other side of the street and is worth a look, although it's always busy (I was lucky enough to be working in there a couple of times, so have had the free tour!!)
There's plenty of ghost tours, some better than others so be a bit choosey - they do offer warnings for some of them, and they are the better laugh (or scare, depending on your outlook). The dungeon is good too, underneath Waverley Station.
Been hearing a couple of good reviews about an "Escape Room" near Holyrood - Can You Escape? Think you may need to book though.....
Dynamic Earth is good too! And take the open-topped bus - it always pisses down in Edinburgh, so why they have no tops I'll never know! Pack warm gear too, as the wind will cut you in half at this time of year!
Enjoy, I love going through there for a weekend, but it's a **** of a city to work in......