Love the Sky Garden, love the views, not completely sure about the slightly difficult booking in advance issues, but for the price of a drink or small snack you can go up to the bars with no reservation. I've always grunted through the reservation system. The webpage takes a bit of practice.
The rooftop at One New Change overlooks St Pauls Cathedral and the City. Absolutely free, absolutely trivial to achieve, out in the open so not so great if the skies open, the first floor has all sorts of restaurants including Nandos, Byron, Wasabi, Eat, Wahaca, and my favourite burrito place, Burrito Mama - a part of Wahaca.
I haven't been up there yet but the roof of Tate Modern - just across the Wobbly Bridge from St Pauls - gets excellent reviews. It is on my list. Free, too. Speaking of the Wobbly Bridge, since it is exclusively pedestrian (and the occasional bike) the views are great up and down the river and no traffic noise or hazards, but it is considerably lower down than a rooftop viewpoint. Good views from the glassed-in Blackfriars Station, if you have reached the daily cap on an Oyster it is free to visit, and you can even take a train somewhere.
The rooftop garden at John Lewis department store in Oxford Street gives a good view of that area.
It has been absolutely ages since I have been up there but you used to get a pretty good view from the Oxo Building.
Good view of Greenwich from the Observatory at the top of the - steep - hill.
Great views - a bit further out - from the Ally Pally, Alexandra Palace.
Or from the top of Primrose Hill, higher than any skyscraper, all the way down to the City and the Shard.
... and there are others....