Florida really lacks any type of short diving. There is a dive site in Bradenton, the Regina, about an hour to the south of Tampa on the Gulf that is a shore dive but it really isn't much.
Here is someones video:
Regina Shipwreck Freedive (Best One Yet!!!!) - YouTube
And info on the Regina:
Regina Sugar Barge - Bradenton Beach, FL - Dive Sites on Waymarking.com
There really isn't a whole lot there and visibility is very hit or miss. There are usually a ton of sand dollars that you can see all over the bottom. I've heard there is a small reef/ledge some where near the outer side of the markers but I haven't seen it. You can hear the crackle so I'm sure there is something there I just haven't searched for it.
Like keller34 said, the other option is a trip to our springs, like Rainbow River or Ginny Springs. Rainbow River is a great option for both divers and non-divers, it offers tubing trips down the river, kayak rentals and more. You could rent kayaks and paddle up stream and drift dive with the current or you can use a water taxi/dive boat (about $35 per person and you need to arrange in advance) to make a trip up. More info about Rainbow River:
K P Hole and the Rainbow River
I have not been to Ginny Springs but have heard it is fun. You can check out the following site for some info:
Florida vacation for scuba diving, river tubing,&PADI certification
If you were looking to go out on a dive boat in Tampa you would likely be heading to the Clearwater area and we would give you a list of some of the dive boats but unless you're planning to leave you non-scuba friends at the beach while you do a morning or afternoon dive trip, that won't be of much help.
I would say that Rainbow River may be a good fit for both you and your friends. It is shallow enough to snorkel, the water is crystal clear but you'll all need wet suits as our springs are 72 year round.
