It is not a terrible neighborhood. There are some parts of Holiday that aren't great but they are not terrible.
You are about 10-15 minutes from Fred Howard Park in Tarpon Springs which is a nice beach.

I would also suggest a trip out to Anclote Key. Head down to the Tarpon Springs Sponge Docks and there used to be ferries out to the Key. You could head out to the island early and have a late luch/early dinner at the sponge docks when you get back.
More info here.
Main Page - Anclote Key Preserve State Park » Florida State Parks
Another day trip that may interest you is Weeki Wachee Springs. It will be about 35 minutes north. You can check out the mermaid show and the animal show and then take the boat ride down the Weeki Wachee River or you can skip that and just rent a canoe and go down the river on your own. The canoe trip would be about 5 hrs so it would really be the park or the canoe trip, no time for both. More info here.
Main Page - Weeki Wachee Springs State Park » Florida State Parks
If you take a trip down to Clearwater Beach you may want to give the Hilton a call first, 727.461.3222, to see what day they have their prime rib and seafood buffet and schedule your trip for that day. It is worth the trip down (35-40 minutes south) for prime rib, crab legs, shrimp, etc.
This should be enough to get you started.