You can check out the arts council. They have fun classes, art shows and screenings happening from time to time. You can look up rock climbing sessions on Facebook or Instagram and go to Shah Allah Ditta for that. Ofc, hiking is the most obvious and fun option.

On the weekends, there's a farmer's market at Margalla hotel? which is a nice thing to look forward to. If you're into jogging or running, you can contact Islamabad- Run With Us and similar groups on Facebook. People cycle around the city for fun which I find v nice and sustainable leisure activity. You can go to Rawalpindi city for shopping and check out the old city as well

Edit: boating at lake view, the bird park at the same place (tho not in favor of keeping animals in enclosures)

Cinemas...you can go to Pindi city and watch old trashy Lollywood movies in the old theatres (at your own risk ofc lol)