You looking for a beach specifically on the Gulf of Mexico, or would a beach on the intercoastal/Tampa Bay suffice?
If it's the latter, then there's a (small) beach within *minutes* of the airport along Courtney Campbell Causeway...it's a little park just west of the Hyatt Hotel...the Hyatt also has a small beach behind it very near their pool.
Hyatt is a beautiful hotel, and there are several others (smaller) across the road (think it's the Residence Inn, etc.).
If you're looking for the REAL beach, then you've got about a 25-35 minute drive heading straight west to Clearwater Beach...a tad south of that is Sand Key...then a little north of that is Honeymoon Island (state park)...some of the most *beautiful* beaches in the U.S.
Any number of hotels/motels along the waterfront there...Adam's Mark (Clw Bch), Sheraton Sand Key, Radisson Suite Resort Sand Key, Holiday Inn Surfside (Clw Bch), Hilton Clearwater Beach,...some of the bigger names.
Google search should turn 'em all up.
Clearwater Beach is big, beautiful and busy...lotsa young people and families...many places to eat, drink and shop. Sand Key is big, beautiful and more quiet...very family oriented. Same w/Honeymoon Island State Park, so it depends on what you want in your beach experience.
Hope this helps...