I live on Skye and applaud your decision to spend some time on our wonderful island.
If staying near Uig you will be very close to the Museum of Island Life. It's a very small museum, curated in a very understated way but done with great love by local people. My husband says it's the best £2.50 you can spend on the island! Nearby is the truly excellent Single Track Cafe and Espresso bar. It's in a very unusual, modern, wooden building with amazing panoramic views out to sea and across to the Outer Islands (where you will just have come from!). The best tea/coffee and cake on the island. On the outskirts of Uig you have an excellent pub called the Ferry Inn. Great food and I believe they also do B&B, so could be a good place to look into. Up in that area you have the Trotternish ridge which stretches from the far north of the island down to Portree. There are good, short walks in the Quiraing and many people also like to walk up to the Old Man of Storr. There are good views of the mainland to be had from the Kilt Rock waterfall lookout point.
Near Dunvegan you will find the Coral Beach - a super place to visit on a sunny day when the water looks so blue and clear. There's a small hill behind the beach, well worth a climb up as the views are great. You are likely to see seals. Dunvegan castle and gardens are also worth a visit. The castle own a good shop called The St Hilda Shop, which sells very good quality souvenirs e.g. tweed, wool and silver items, as well as books and cards. It's just along from the castle on the way back into Dunvegan.
If you are staying in the Dunvegan area you will also be in reach of Neist Point lighthouse, the most westerly and one of the most wild places on the island. You can walk on a paved path out to the lighthouse, although there are many steps to tackle, or you can take a short walk along the cliff to get great views back across to the lighthouse. There are a pair of sea eagles that frequent the area, and you may see dolphins and whales from the cliffs - bring your binoculars if that sort of thing interests you.
Dunvegan would also be a good base for foodies, as you can eat at the Lochbay (Michelin star but not too expensive) in Stein, or a new place The Edinbane Lodge, which is fine dining without the price tag. There's also a good pub in Edinbane called the Edinbane Inn. Dunvegan itself has the Old School Restaurant which is good. There's also the Three Chimneys in Colbost and The Red Roof in Glendale, which is a 'croft to table' restaurant offering very locally produce on a 'no choice' menu - always excellent!
You are focussing on the north of the island, which is fine if you don't mind missing out on the mountainous scenery of the Cullins in the south of the island. However, you could easily do a day in the south from either Uig or Dunvegan. There are wonderful boat trips from Elgol on the Bella Jane.
Let me know if I can help you any further.