Inverness or a town near it is great base for day trips. I've done both. At that time of year, I would probably lean toward staying in Inverness as places do start to close as you move toward the end of the month.
Now for the hiking--or walking as it is called in the UK! Have you found the website WalkHighlands? It's a great resource. You can only town and village website to see what walks are suggested. You can see that it is sorted by region. Pick the Highlands and then look at Loch Ness, Glen Affric and the Black Isle. One of my favorite walks is in Glen Affric. I've done the walk around the Loch which was a day hike and I've just walked in and back out. It's a beautiful Glen.
To see the walks near Nairn, just the Moray section. Culbin Sands is near Nairn. It's forestry land and has wonderful walks along the coast of the Moray Firth. In early fall you see lots of sea birds and seals.
You can get to the west coast for day trips. You will less light, but I bet you could still do one if you wanted to. Ullapool might be a good one The town is interesting and there are some nice walks in the hills immediately behind the town.
Another west coast possibility is Torridon. It's a beautiful area. (Well, to be honest, all of Scotland is beautiful to me.) You might find Applecross is too far with the light, but Gairloch is doable.
If the weather in the west disappoints, think about going North along the coast. Dunrobin Castle is right on the Coast. Look in Dornoch, Lairg and East Sutherland section.
And of course, you could go south to the Cairngorms. The Rothie Murchus Estate has lots of trails.
If you want to walk you will want to pay attention to the weather. Also, I would strongly recommend walking boots if you are going to go off-road and on trails. I love Scotland, but it's a boggy place. :)