Bermuda lodging
 

What resorts are recommended for two 40-somethings who want peaceful spot with ocean terraces, access to restaurants, sights and shopping. Budget of about $300/nt, don't mind cabs to get around!

The Reefs is beautiful and exactly what you want except the price.
When we went, dinner and breakfast were included. You may be able to get just breakfast.
Buses are a great cheap way to town. Mopeds are fun. And of course, cabs are plentiful.
The Reefs is a smaller hotel/resort which caters to adults more than families,and has very good food and is nice.

The Reefs has been under some renovations - not sure if they are complete. Look at Coco Reef - smaller, but closer to things and laid-back. What time of year? Do you want ocean views or actual ocean frontage/ beach access? Are you looking for just a room or some more amenities?

Pompano

If you have a sense of adventure, consider renting mopeds instead of relaying on cabs to get around. I know that the 'dangers' are often publicized but we've rented for a week or more three times with no problems. It offers alot of freedom to really explore and find the out of the way beaches and have a way back without waiting for a cab or bus. We love Elbow Beach but its gotten quite spendy and I think that they require MAP which would blow your budget. Do a search on hotels.com and see what shows up. We stayed last time at Grape Bay and basically used it for a base - didn't use their pool or beach - just slept there and scooted all over. You might also find a condo on vrbo.com that would work out.