You can get to a lot of places by public transportation; the difficulty is, what do you do once you're in Oban, Portree (Skye), etc.? West Coast Motors runs 2- and 3-island day-trips out of Oban (ferry-bus-ferry). There's at least one company running bus tours on Skye, and there's some public-bus service. The challenge is the weather, which is very changeable and tends to be rainy. A lot of the transportation needs to be pre-booked at least a bit in advance, and some things well ahead of time. Therefore, you don't have a lot of flexibility to use a nice-weather day for outdoor activities away from your base and a bad-weather day to see the inside of a castle. I have no idea what happens on a multi-day tour like those Rabbies offers if the weather is pouring down one day. Do they proceed with the original plan, or do they tweak it? How much outdoor time is planned on those tours, anyway: Are you given enough time to walk to places like the Fairy Pools and the Fairy Glen on Skye?
Edinburgh, Glasgow, Dundee and St. Andrews can be easily visited without a car. I based in the first three. I went to Rosslyn Chapel from Edinburgh by public bus on a nice day and to St. Andrews from Dundee, also by bus, on another nice day. Stirling Castle can be seen from either Edinburgh or Glasgow. So I'd recommend a few days seeing the urban areas of interest to you and a tour (Rabbies or other; Rabbies does have a great reputation here) for the rest of your time.