Can I just buy tickets for London Eye/Tower and so on at a tourist information center in London without having to go the attraction and wait in line?
I'm not sure about buying them at a TI office, but many can be bought online. Just go to official website for the attraction you are interested in. For things like the Eye you are buying a specific date/time ticket. Don't know if that makes a difference in your plans. If you get to the Tower of London early (just before it opens) you shouldn't have to stand in line. Then go do the jewels,and after that do a beefeaters' tour. That's the most effcient way to see the Tower.
We have purchased The London Pass which covers your admission for many places and also includes a "fast track" pass which lets you skip lines at certain places (including the Tower). I don't think that they London Eye is included though.