In reply to Matt Rees:
The main 'tourist track' from Brodick going either via the castle road or past the brewery is the obvious way to go, but I find it much more enjoyable to include North Goatfell, the saddle, and Glen Rosa (either on ascent, descent, or both).
To be honest almost every other hill on the island is actually of more interest. Depending on your scrambling ability, consider starting off by getting the bus to Sannox and heading up Cioch na Oighe, and along that ridge to Goatfell.
Cir Mhor is an excellent choice if you like being out of breath (it's exceptionally steep). But if you head left from there along that ridge you'll have to contend with some rock climbing for the a'chir ridge (which is perfectly doable in trainers if you are of that mind). Similarly if you turned right you'd need to take on the witches step. Trainers still work fine but I strongly recommend heading East along this ridge, never West!
Give me a message if you want more info on good routes or want to meet up for a run/walk/climb.