Clearwater Beach is a lovely option. Clearwater Beach is a compact area with hotels and restaurants in the main area. There are not many short term condo rentals due to municipal bylaws.
How long are you planning on staying? Two places that allow weekly rentals right on the beach are Villas at Clearwater Beach and Surfside. Colony Surf allows two week rentals. I'm not familiar with these buildings - so can't vouch for them. I do know that Villas and Surfside have three bedroom condos.
Right over the bridge on Sand Key - Lighthouse Towers and Crescent Beach Club allow two week rentals. There are two bedroom condos in these beautiful high rise buildings - and you might find the odd two bed and a den available for rent. We own in Crescent Beach Club and it is beautiful. Sand Key is a semi-private beach - so a lovely place to stay for peace and privacy - but you would need a car to get to restaurants.
The area between Sand Key and St. Pete beach has many condos available for short term vacation rentals right on the beach - due to different bylaws. Check out Belleair Beach, Indian Rocks Beach, Indian Shores, Madeira Beach, St. Pete Beach and Treasure Island.
To find vacation rentals check out VRBO, vacationrentals.com and Trip Advisor Vacation Rentals. Look for units that have reviews and check out Google maps for location. Also post on the forum for those areas if you find a place, and ask for help on what the condo complex is like. Rentals from owners are buyer beware. We have rented through VRBO many times and never gotten scooped - but check out the rental well and talk directly to the owner. You could also go through a vacation rental company - but prices will be higher than they will be directly through the owner.