Two days is pretty hard to get to the place of action, and back again to London AND have some time to see some stuff inbetween. Getting to and from Glasgow or Edinburgh isnt the hard thing, but its the transfer to where you want to be afterwards ...
The Speyside might be an option, but depending on what flights you take, you might even try Islay if you can get a proper connecting flight after your arrival. The density of distilleries on Islay allows for heaps of fun ina single day as well. But you'd still want 2-3 THE MINIMUM on the island itself.
If you really want to go up north and taste a little of the Scottish life, then I can whole heartly recommend Edinburgh! This city simply rocks. Visit the castel, the roral mile, with the most famous royal mile whisky shop, the Whisky Heritage Center, some of the classic whisky bars, and if time permits, you could go and visit Glenkinchie. I did that once with public transport, but the ride will take some time, so this is preferably done if you have 2 full days the minimum.
Glasgow maybe has access to a few more distilleries (glengoyne and Auchentoshan are the only ones that come to my mind that are close enough for your timeframe, but even then, Glengoyne still needs quite a ride on the bus (line 10 IIRC)), and to be honoust (I hope I dont get fried by Glaswegians (Hi Iain!)) personally I dont like Glasgow that much compared to Edinburgh. If you like a good nightlife you'll have a good share of fun in Glasgow however.
Hope this was of some use to you