Lots to do in an around Tucson. Previous responses point you in the right direction. If you've never hunted javelina before, I suggest you spend your first day in Tucson at either the Arizona-Sonora Desert Museum or the International Wildlife Museum. There you can see live and mounted javelina. This will help you develop a search image for your hunt, so you recognize them when you see them. I think that's the hardest part about learning to hunt them - their shape and size are really different from other game we hunt.
Another cool place not mentioned yet - Pima Air Museum. Also Kitt Peak Observatory if you're into that. Kartchner Caverns is neat. Wish I could recommend some good resturants, but the places where I ate back in the day may not be good anymore. For Mex I guess you can try Mi Nidito, El Torero, El Parador, El Charro... no promises now but they used to be good. And El Corral has pretty good steak and prime rib.
The THING.... you'll drive by that about 1 1/2 hours east of Tucson on your way to the hunt... I guess you can stop at the Dairy Queen and have ice cream.
I'm not too familiar with 28 so cant help you there.
good luck