For such a small area the British Isles are incredibly diverse.

I would recommend you visited Scotland and in particular the north west coast. The Isle of Skye is magical but can be a bit overrun with tourists in places, I love The Cuillins and always spend a day there when on Skye. Applecross on the mainland is worth a visit and the Walled Garden restaurant is a must visit. There is a route around the entire north of Scotland called the NC500 but I think the highlights worth visiting are all the west coast side. Maybe do some island hopping over to the Outer Hebrides, Calmac ferries provide the service. The sea food on the west coast is amazing, a particular favourite of mine is fish & chips in Mallaig, so so fresh as they land the fish there.

Southern England is great and I'd recommend heading to the Isle of Purbeck and heading southwest as far as you can get. Devon & Cornwall are incredibly popular in the warmer months so you may want to avoid.

London is utterly fabulous IMO but isn't everyones ideal location and can be truly expensive. Some great eating experiences, shows, music, museums.... it has it all really.

The rest of England has a lot to offer too, the national parks are all worth a visit - The Lake District, Peak District etc.

Wales is splendid, in the north is Snowdonia and its rugged hills/mountains. South Wales is interesting especially its industrial past. Great roads.

Ireland is worth a month or 2 on its own! I lived there for 4 years and didn't see it all. I loved the west & south west coasts, these areas felt different to the rest of Ireland.