Here's my current situation:

Level 19
Main quest finished up to the beginning of the final mission
Plenty of miscellaneous quests and exploring left to do

I want to finish the other quests and explore the map some more before finishing the game, then I want to move on to the expansions. My question is, should I install Broken Steel now to raise the level cap to 30? Otherwise it seems like I'll be throwing away a ton of experience, since I'm already halfway between Levels 19 and 20.

Is there anything else I should be aware of? Does installing Broken Steel change what's left of the base game experience? Or can I just get the increased level cap now, and wait to use any of the other features?

Thanks!

Go for it. All it does is raises the level cap and extend the main quest. It won't touch anything else, aside from adding in a few NPCs and locations.

Other than the level cap, most of the things it adds to the base game don't kick in until after you've finished the main quest and/or reached level 20. So there's really no point in holding off on installing it.

I would install it immediately although watch out for the Super Mutant Overlords those things are a (Censored) if your not careful.