As mentioned above, the drift-diving scene off of Jupiter and West Palm Beach, is really good, not real expensive, and a good contrast to the usual out-and-back dives off an anchored dive boat. You're at the edge of the Gulf Stream, so the boat starts at the southern end of whatever particular reef, and both divers and boat drift north in the 1-2-knot current, typically there's a DM with you trailing a surface buoy for the boat to follow. So ascend whenever you like near the buoy line (don't hold on to it, the DM will not forget it if you do, it's a free-ascent), and the boat's there, or not too far away from the buoy. Just give them the signal, and they'll come get you, maybe some others first, so just lie back on your inflated BC and enjoy paradise.
I've dived Oriskany three times. First time a few months after she was sunk, still a "gray ship", flight deck at 130, and tower topped out at about 65-70 as I recall. So intermediate divers were mostly in that tower, nice swim-throughs. And some of us (meaning me) went down to 129' just long enough to touch the deck with your finger so you can say we did it, and feel like tough guys when we wrote it on our log books ;-) Yes, nitrox definitely a good idea.
Second time was a couple years later, she had shifted in some storms and listed deeper on the tower side, so deck was like 140 or so, and I wasn't going that deep So we doodled around the nav bridge and the Admiral's bridge in the 100-110' range. She was now a 'brown" ship, not much gray left anywhere.
Third time a couple years later still, and she had settled a bit deeper, so those tow bridge decks were about ten feet deeper. Definitely a "ship of the deep" by then, lots of marine growth, more like a high-tech reef.
Very good diving, but not really for the novices at the top of the tower any more. Nearby I recall there's another structure, a cut-off oil rig leg structure (the Chevron Platform), at about 90'. That might be your second dive of the day, since shallower.
Yes to shore dive at Phil Foster Park aka Blue Heron Bridge. But check your tide tables first, you can only dive it at the high tide, so you want a midday-ish high tide.
My Oriskany experience is kind of old. But the Jupiter and West Palm, more recent.
I've dived more often at Orange Beach and Pensacola, lots of things to look at. Mostly wrecks and bridge rubble (which sounds unglamorous but it's really pretty nice with all the nooks and crannies for marine life). Check with them when you book to see if it's going to be an "inshore dve" (about 3-4 miles out, wrecks sitting on about a 50-foot bottom, so good for newer divers), or an "offshore trip", about 10 miles out, wrecks sitting on about 90' sand. Oriskany is a few miles farther out, and is a "long day".
One note of caution right now--they're getting pummeled as we speak, by Hurricane Sally. Give them some time to get repaired and back in business. I hope they all come through okay, they're good folks. The ones I've dived with most are Down Under Dive shop in Orange Beach, and ScubaShack and MBT Divers in Pensacola. It's kind of cold in winter so not many trips, but from May through October, lots of trips.