It's been great weather all this week - it can't last though
Here's another useful link - www.aboutbritain.com/towns/Aberdeen.asp
There's a huge leisure complex on the beach with swimming pool with flumes, jacuzzi, gym, ice rink and there is a creche. Nearby is also Codona's amusement park, a cinema, cafes, restaurants, nightclub etc ... and of course the beach itself if it is warm enough!
For music/arts try the Lemon Tree - is a small venue which has bands playing most evenings and also some lunchtime shows which allow children. There are also some theatre shows and workshops for children over the summer. The Lemon Tree is in central town. They have a cafe as well.
Aberdeen also has a theatre, art gallery, football stadium, 2 universities. Aberdeen University is the oldest (over 500 years old) and worth a visit. The maritime museum is interesting and the harbour itself (all within walking distance of central town). Marischal College (part of the uni is the 2nd largest granite building in the world). In fact most of the buildings are granite hence the name 'The Silver City'. Storybook Glen is great for the kids (theme park). Other good parks are Duthie Park (with Winter Gardens) and Hazlehead (which has a small zoo). As you'll probably know Aberdeen is bordered with 2 rivers, north and south with nice walks alongside. There are more swimming baths in central town - these are huge and built in the 1950s. Also you can drive 15 miles south to Stonehaven - a small town on the coast which has an olympic sized outdoor swimming pool (and it is heated!) - the only one of its kind in Britain - see www.stonehavenopenairpool.co.uk/index.htm
They also do midnight swims. Stonehaven is a lovely tourist town to visit. While you are there also visit Dunnottar Castle which was the location for the film version of Hamlet starring Mel Gibson. Also see nesting gulls here ...
Not too far away is Balmoral Castle and masses of other castles to visit - see www.castles.org/Chatelaine/list.htm, also distilleries (over 40 - you can do 'The Whisky Trail' ) or you could take a bit more time and drive up to Strathspey and go on a steam train. There are also plenty mountains to climb. Oh I could go on - you'll need a month to see everything!