besides the eye(s)

The top of St. Paul's Cathedral

The viewpoint on top of Parliament Hill Fields (public park in North-West London a little out of the centre).

I second St Paul's cathedra. And it's an amazing experience to go up inside the dome.

I third St. Paul's Cathedral. If you can manage all those stairs without keeling over, the view is amazing.

I've also been told that the view from the Westminster Cathedral Tower is really good ... and there's an elevator! (Note: Westminster Cathedral, not Westminster Abbey.)

The Tate Modern has a nice cafe on the 7th floor, with a great view across the Thames looking toward St. Paul's. You can get a meal or just a cup of coffee.

My daughter and I climbed the dome at St. Paul's last August; it's a wonderful view even if you only make it to the Stone Gallery [the second level and the first outside gallery], as I did. The stairway to the Golden Gallery was too open for my acrophobia... but DD really enjoyed getting all the way to the top.

Remember, the Eye is only a few minutes at best.

Oxo tower, Tower Bridge (Tower Hill tube stop), Primrose hill (Chalk fFarm Rd tube stop, northern line)

Another advantage to St. Paul's- you can check out the whispering gallery on your way up.

The Monument! It's a cheap option, but only for the nimble of foot as it's a steep staircase with limited room for passing.

I've got some absolutely lovely scenic shots from The Monument, and it has a great view toward Tower Bridge.

Well worth the admission fee (3 pounds?).