Cornwall coast or Lake District?

What do you like the best: coastal scenery or mountain scenery (small mountains compared to Rockies or Alps)?

I would choose both! I adore them both and they both really deserve a look, especially if time is not an issue.

Yep. I was trying to get an answer from the OP.
Maybe they'll be back.

The choice is a personal one and depends on how much time you have. The weather should be OK in September for both, but as they are both to the west of the country, they will generally have more rainfall than London in the east. They are both green counties for a reason (i.e. rain)!

Cornwall is about half as big again as the Lake District but is generally easier to get round as the roads are flatter and generally wider. The Lakes can take ages to make any progress on the roads, so if you only have 2 or 3 days and you are already in Bath, I would say go to Cornwall. If you have a week, I would go to the Lakes.

Cornwall is all about the scenery and the coast. The architecture is on the whole drab for your average house there. The Lakes have more interesting architecture but is hilly rather than coastal. The Lakes coastal towns to the west are functional rather than attractive, so best avoided. Stick to the inland lakes villages and the hills. You will need a car for both.

The National Trust has interesting houses in both areas if you want a bit of history. Plenty of accommodation in each.

If I was in the Bath area, I would go to south Wales, which has a mix of old ruined abbeys (e.g. Tintagel) to the shops of Cardiff, to the hills of the Brecon Beacons, to castles and old gold mines and some of the best beaches in the UK - The Gower and Pembrokeshire.