Access to the Sky Garden is free of charge on weekdays 10am-6pm and weekends 11am-9pm. You do have to book your spot online.
TimeOut has interesting suggestions for other roof gardens, if you want to give the Shard a swerve: https://www.timeout.com/london/things-to-do/the-best-rooftop-gardens-in-london
Hidden gems: there isn’t much “hidden” in London these days, but if you list some particular interests, there are plenty of folks on this board who would have info on less touristy spots, or places you might not have thought of.
For example, I have loved visiting Freemason’s Hall, near Covent Garden: https://www.ugle.org.uk/freemasons-hall
For cool gifts, the Royal Opera House (in Covent Garden) has a classy collection of wonderful things that make excellent gifts that aren’t in the “red bus - police box - Paddington - Tower Bridge” wheelhouse but are also very specific to London. (Same goes for the gift shop at the Globe.)
The North End Road Market in Fulham is very local and untouristy, with a distinct London vibe. Lots of interesting little local shops, great fruit and veg, fishmongers and butchers… it’s cool: https://www.lbhf.gov.uk/business/markets/north-end-road-market
The best fish ‘n’ chips in London (IMHO but honestly, it is GREAT) does serve tourists, but I rarely see it listed other places, so call this one a “hidden gem:” The Golden Union, 38 Poland Street. It is right off Oxford Street and steps from Liberty London (and Carnaby Street) so you can visit those more mainstream places and have an incredible lunch.