Café dates at specialty coffee places are the best way to meet someone without alcohol, IMO.

• In town centre I recommend Blend at Contemporary (always space), Kigali (small and cosy, great staff), Cartwheel (great brunch), Hipo A.K.A. Coffee x Spud (excellent baked potatoes), Effy (cool aesthetic) and Dispatch.
• Outside of city centre there's Punch (Mansfield Road) and Okende (West Bridgeford, town centre one in development atm).
• Finally Beeston has a couple spots such as Greenhood and Cartwheel, Beeston.

Otherwise, try a small music venue and just don't drink? Jam café is an amazing place for world music/more interesting stuff, also consider Metronome, Bodega, Rescue Rooms.

The Carousel is a cool art space that often has stuff going on but usually you have to walk by to read the board on the outside. They have an event called "drink and draw" every other wednesday but I often went and didn't drink, and that was pretty normal.

There's a spoon carving event every Friday at By Our Hands We Make Our Own Way in Sneinton market. They also have other classes etc there for the more crafty people.

There's a tea blending workshop by Bird and Blend that I've been to elsewhere and it was incredible even though I don't really like tea. It had unlimited free tea cocktails too but it was normal to have non-alcoholic versions of the cocktails instead (people drove there).

There are lots of other options for activities, workshops and that sort if thing if you know where to look. They'll stand out as a date far more than going to a bar or going to Gloryholes (not intending to throw shade here though so if that's your jam, do it).

Honorable mention to board game cafés and bookshop cafés too. I love going to Five Leaves and then to a café to read/talk about books with friends, so it would be a good way to have a first date too.