To tour the whole island, but no further, then any base on the A87 will probably do, since it is the main road running through the island from the Skye Bridge to Uig - that drive in itself takes 1 hour and passes right through Portree. The benefit of being located close to that road is that at the end of a day touring tiny single track roads, at least the last part of your journey back to your cottage is on a two-way main road that's easier to drive.

For those wanting to walk/climb in the Trotternish/Quiraing/Old Man of Storr region, then staying close to Portree/Staffin would be ideal.

If you want to stay within the Cuillins area then staying closer to Broadford is probably your best bet.  This would allow for an easy drive down to Elgol and also Armadale, where there are lovely walks with unbeatable views across water to the Cuillin mountain range.  This is only a 20 minute drive from the Cuillins themselves, at Slicachan and a bit further on to Glenbrittle (about another 10/15 mins), where you are right in the back end of the Cuillins (and close to Talisker Distillery too!).

For those wanting to tour some of the Wester Ross/Lochalsh area as well as Skye (eg. Glenelg Peninsula, Eilean Donan Castle etc.), then you want to be based again close to the A87, but nearer the bottom end of the island - Broadford, Breakish, Kyleakin, or even Kyle just across the bridge on the mainland (note the Skye Bridge is now free, no more tolls). From here you can easily tour the top end of the island.  A drive around the Trotternish Peninsula (Portree, Old Man of Storr, Quiraing, Duntulm, Uig), is roughly 2.5 hours from the bridge.  Another option is to drive around the Applecross Peninsula on the mainland for instance, taking in some fantastic places like Applecross Pass, Shieldaig, Torridon, Loch Maree, Loch Carron & Plockton to name just a few! 

Travel times:

Kyleakin (Skye Bridge) to Broadford (9 miles) - 10 mins

Broadford to Armadale (17 miles) - 20 mins

Broadford to Sligachan (17 miles) - 20 mins

Broadford to Elgol (14 miles) - 30 mins

Sligachan to Dunvegan (23 miles) - 25 mins

Dunvegan to Portree (22 miles) - 30 mins

Sligachan to Portree (9 miles) - 10 mins

Portree to Staffin (16 miles) - 20 mins

Staffin to Uig (via Duntulm) (17 miles) - 30 mins

Staffin to Uig (over Quiraing) - 20 mins

Uig to Portree - 16 miles (20 mins)

These times should give an idea of distances/times from most main points on the island.   Remember some distances take longer to drive than they look like they should (eg. Broadford to Elgol) simply because they involve single track roads. Basically, any other roads, branching off from the main roads metionned above, do reduce to single track.

** Note:  The original information for this thread came from the following forum thread: http://www.tripadvisor.com/ShowTopic-...