The Clearwater Sailing Center on Sand Key, it cost $10 to launch there if you aren't a member, memberships are just under $400 a year. And the Dunedin Causeway in Dunedin, AFIK it's free to launch there but it is the furthest away from you.
The Clearwater Sailing Center is much more than $400. It is more like 1200 to keep a catamaran there (they actually charge by the foot). You must get a full family membership (around $800 if memory serves) and then pay for the rental space (around $400). I may have those figures backwards... I looked at it 3 years ago and was a bit surprised at the costs.
The Dunedin causeway is free to launch, but required a weekend permit ($10) for overnight (weekend) or $100 for an annual permit. This allows you 2 nights mast up per week. There were complaints from local residents, and more so from local police that put the permits in place. Originally was going to be 2 nights per month, but we got involved and worked with the town to increase that to 2 nights per week.