The Gulf coast will be more like a 2+ hour drive. I used to live almost exactly halfway between Clearwater Beach and St. Pete Beach and it always took a little over two hours to drive to WDW or to drive home, and that’s if there are no traffic issues. We very rarely would do a day trip just because of the drive, although we generally stayed off property back then. You aren’t going to find a beach under two hours drive unless you go to the Atlantic side.
Once you get there, though, the Gulf beaches are fabulous. If you are looking for quiet, you might want to consider some of the smaller communities instead of Clearwater or St. Pete beaches. I have stayed at Sand Key, Indian Rocks, Indian Shores, North Redington, and Madeira beaches, and they all had moderate crowds. As you get into Treasure Island and farther south toward St. Pete, the beaches get busier.
Another nice beach area is Fort Desoto Park, which is a group of undeveloped islands. There is a campground there, but no hotels. We used to spend the day there, and it was rare to see more than six people all day. The park is right at the mouth of Tampa Bay, so there is water everywhere. You can rent canoes, kayaks, and bicycles as well. Depending on when you are going, if you choose Fort Desoto, you might want to check the Pinellas county parks online to see if everything is business as usual.