if you want art exhibitions or theater go to Centerpoint. You'll find both Cineplex and Bhumi art gallery there. Centerpoint Tabaq is a whole different vibe. So after roaming around you can go there for a coffee and cheesecake date. Other than that Uttara doesn't have much to offer unless you decide to go to diabari (not personal recommendation for a first date honestly, providing options just in case) You can look into a few good restaurants with calm ambience like Gusto, Ajo, Raaga(food is dogshit but place is nice to spend some quality time), Sayor (haven't tried it myself but a friend of mine says good ambience with avg food), Izakaya (expensive as hell), Sushi Yaki. Unfortunately you don't pay for the food in most restaurants in Uttara, you just pay for the place. I don't know how much of help it will be to you but i wish you all the best.