But I wouldn't expect much progress in the next 200 years.
I'd be much happier if they just threw some serious resources towards former astronaut Franklin Chang-Diaz's VASIMR propulsion system:
http://www.spaceflightnow.com/news/n1006/01vasimr/
That's doable, right now.
Fission power on spaceships - that's doable, right now.
Fusion power on spaceships - hopefully that's doable within 30 years.
Get to 1/10 the speed of light this century, and I'll be impressed. 1/2 c, and I'd be floored.
Get to work on antimatter as a way for storing energy for starships - I'll be even more impressed this century.
http://www.space.com/17537-antimatter-fusion-engines-future-spaceships.html
(although this technology would probably be commandeered by the Generals for awesome weapons - let's not destroy Humanity before we reach the stars, shall we ?)
This century, if they can get some spaceships to the Kuiper Belt (30 to 50 AU away from Sun, about 7 light-hours) - I'll be happy.
Faster-than-light travel - if they make NO progress till the 22nd century, I won't be surprised.