I once spent 25 days in St. Croix. Everything is on island time. Don't get into a hurry. St. Croix is like Dollar Tree Puerto Rico. There are some cool places to see and enjoy, but you have to work for them. I remember it fondly, but I would not go back. Had scabs and scars from the bug bites for 6 months (wear repellent).
Good roasted island chicken place (La Reine) on Northside St, just north of Centerline Rd. We called it Chicken in the dirt, ate there probably 10 times. Appears to be pretty popular now. Red barn-like appearance, right off the road. It might take 30-45 minutes to get your food (everywhere, actually, even Wendy's). Plan ahead.
There are some decent bar/restaurants in Christiansted. One place (Rum Runners?), there was a guy who would take hot dogs and throw them to the tarpon just off the boardwalk. I have never seen an animal track and move as fast as those giant fish. Quite amazing.
I had rented a jeep and took it all over the island, there are some cool dirt roads thru the hills that were fun to drive, easy enough. The jeep was left drive (like normal) but you drive on the "wrong" side of the road. It's confusing. But you'll be driving really slowly anyways, because there is always someone in no hurry in front of you.
For activities - I went to East Point (easternmost point of the US). I drove to Sandy Point (western most point on the Island). I hiked to Hams Point lighthouse (not a long hike but pretty). I sat on the beach and watched the sunset. I kayaked around Green Cay. Mostly, though, I drank a lot. Working 15 hours per day and generally only getting Saturdays off. If I went now I would dive. Buck Island is pretty.