Are there any TV’s that convert to 60fps?

TVs can show 60fps from 60fps content. But many newer TV can upconvert (sort of) from 30 or 24 to 50.

Many newer TVs have this capability (I think most new Samsung, Vizio and LG) and call it different things (Vizio calls it Smooth Motion)

Some of them simply repeat frames and some make a "guess" of what the picture would be during the "in between" frame, so read up on the brand. I would think that predicting the in between frame would give better results than simply repeating a frame, but I haven't really seen comparisons.

Most people seem not to like this effect and turn it off (I think manufacturers are now turning it off be default, but maybe not) but you might enjoy it. It is often referred to as the Soap Opera effect.

all modern tv sets are capable of displaying 60 frames per second, however the content providers won't supply this. The standard for the UK is 25 frames per second and the American standard is 30fps. The standard for films is 24 fps, as this gives slight motion blur which is often considered good for film/tv content. 

It's only places like YouTube where you might find 60fps content, as the content on YouTube often comes from individuals and not professional media companies.

It is possible to convert 24, 25 and 30 fps to 60fps, however this isn't something we will see any time soon on the big screen.