Getting to Skye by public transportation will not be a problem. Getting around the island once you get there will be a problem. There is bus service, but it's not frequent, so you could end up being stranded somewhere you're visiting until the next bus comes by. The buses mainly operate on the main roads between Kyleakin, Armadale, Broadford, Portree, Dunvegan, and Uig. However, if you want to get off the beaten path, you'd need to take a taxi or go with a tour group.
Talisker is the only distillery on Skye, and is a good one to visit. However, you really don't need to visit a lot of distilleries, as the distillation process is fairly uniform. The water used, and the casking, really make the difference. Several posters here recommend Edradour, outside of Pitlochry, which is easily reached as a half day trip from Edinburgh or Glasgow. Your husband will have plenty of opportunity to sample single malts in every pub that you visit. Good thing you're not driving!
As far as choosing between Edinburgh and Glasgow, as Kathleen pointed out, Edinburgh is best visited for history; Glasgow for fun. There is a lot to see and do in each city. I have a personal preference for Glasgow, as it's more working class, and less tourist oriented. But that's just me. If you have enough time to spend in Scotland, you could base yourselves in both.
If you're staying in Edinburgh, the liveliest place to stay would be in one of the hotels in the Grassmarket. There are lots of pubs and restaurants within walking distance, and the pubs and restaurants on Rose Street are a short taxi ride away.
In Glasgow, your best bet would be in the central area, around George Square, are there a lot of late night venues in the vicinity. A couple of the best music venues in Scotland (King Tut's Wah Wah Hut and the Barrowlands) are only a short distance away. Another good location would be out at the west end, near the university, somewhere off of Byres Road. Again, lots of night time activity.
Hope that's a start. Best wishes for your travels. Next trip (the one after this), spend the whole holiday in Scotland!