Not for baseball, but been to the general area a few times including Dunedin at about this time last year.
Used a couple different beaches for very different experiences that are each good in their own right....
Honeymoon Island is very natural. Intentionally undeveloped for the most part, pretty rocky in most areas but plenty of spots to setup and relax. Clearwater Beach is more developed and has a great white sand beach, pier, more stores/eating options, etc. If you want to go a little further down the coast from Clearwater Beach, more beach options and a nice little area called John's Pass that's fun for its shops/restaurants.
If you have a car (or don't mind a pricey cab ride), its a bit of a haul into Downtown Tampa but its a fun area to spend part of a day. We liked the Florida Aquarium and their waterfront area. Nice little outdoor mall with restaurants to grab a bite to eat and the hockey arena is right there. Depending on the opponent you can get tickets for a pretty good price compared to what one might be used to paying here.
Last year we stayed at Coconut Villas (link below). Checkin was a little weird (phone a number when you get there and they give you a code), but excellent value ($200ish per night at that time at least) for the amount of space you get (basically a small apartment) and location (right on the water, short drive to beach):
https://www.tripadvisor.ca/Hotel_Review-g34187-d1523526-Reviews-Coconut_Villas_of_Dunedin-Dunedin_Florida.html
Looks like you're not far from where the Blue Jays play if you stay right at Clearwater Beach. Lots of hotels on Expedia, hopefully a few folks out there locally with experiences. Hyatt is newish and great location but has been a little too rich for my blood when we've searched. Stayed at the Wyndham in the past, which was nothing special but respectable for price/location (right on the beach stretch).
Would be interested to hear peoples' spring training experiences too!