There are lots of small private hotels in Bermuda, both in Hamilton and outside. These are much better than the resort hotels. Best to check reviews on TripAdvisor to get a wider set of opinions.
Public transport (buses and ferries) is the way to travel (scooters can be dangerous if you're not used to riding one, and car hire is expensive). Check the website -
Bus Routes and Schedule | Government of Bermuda - for schedules and fares - best to buy a one month pass (or one week if you're there only a short time).
The Covid-testing and travel authorisation requirements are constantly changing (generally easing) so check the Government website ahead of time:
Entry requirements - Bermuda (British Overseas Territory) travel advice - GOV.UK
Happy travels!