Go ahead and go, go anywhere and everywhere...
But actually DO something once you get there, don't just go there to wave your dick around.
I'd really like to see a good sized radio telescope built on the far side of the moon, complete with relay lines to dishes at the terminus between near and far sides, so there's no accidental reflections from earth off of relay satellites instead.
Going further out than LEO would be good also...
I remember reading this PDF of a flight plan from around 40 years ago, where they wanted to send a crew further INTO the solar system, and actually intercept/orbit Venus, using apollo tech.
http://en.wikipedia.org/wiki/Manned_Venus_Flyby
How about a small, self sufficient station at L3?
You'd need a couple of relay sats for comms, but that's a smaller cost than the station.
Alas, none of this will happen though, because we're too adverse to risk these days, and we wouldn't DARE send someone condemned to death out there instead, it'd de-demonize them (serial killer and first man on another planet?).
Plus, have you noticed that most of the studies about going into space for long periods of time involve seeing if people can do with limited to no social interaction?
Yeah, most of US can, but the ones they trust to send up there, CAN'T!
So we gotta settle for unmanned probes.
So fire off at least one every month.
Pick something to study: moon, planet, propulsion tech, comm tech, interstellar phenomenom (this one will take time and would need to be fast).
And if you need some tech to make sure it works (such as an RTG), and people complain about it, ignore them with extreme prejudice.
And more space telescopes!
Seriously, we have barely a handful pointing outwards, but probably hundreds (classified, guess, and hope you're not accurate) looking back down?