You can check on your relationship progress % in the stats menu, under "Achievements." She will start inviting you in for "coffee" when you reach around %50. And she'll give you a special gift when you reach 100%.
There are 4 types of dates with Denise:
1-She asks to eat someplace = take her to any local fast food joint
2-She asks to go dancing = take her to the only dance club in LS, marked on the map (the dance club icon only appears when you're on a date)
3-She asks to go driving (not a driveby, just driving) = drive around her house, at any speed, till her fun meter fills up.
4-Alternate date: Denise will almost always ask to do a driveby. If for example, you don't want to take her dancing, just drive around, letting her shoot at rival gangmembers. If she shoots enough of them, she'll ask to go home and the date will be successfull. But don't take too long on this date (or on any date), or she'll get bored and the date won't be successfull.
So unless you want to do this alternate date, just ignore it when she asks to do a driveby. For doing drivebys, just take her anywhere where there are rival gangmembers around (any gangmember not wearing green), which is everywhere in LS, so finding gangmembers for her to shoot should be no problem.
Make sure to save before going on a date, just in case the date doesn't go well. If it doesn't go well, just reset and try again. For more help, read the "Girlfriend FAQ" in the GTA SA section of
www.gamefaqs.com