You'll need a constant power supply for the entirety of the trip. After doing the math, it turns out, fission seems quite viable - all usual fuels, in storage, have half-lives of more than 10,000 years.

So, if you have enough fissiles for keeping the closed ecosystem happy for the duration of the flight, you can go quite far.

The ship/colony will need to enter orbit around a star and drop by a rocky planet at some point, to gather more fissiles and reaction mass (and other materials needed for fixes and upgrades), so it wouldn't be able to stay indefinitely in deep space. If it's fusion-driven, a gas giant may be a good option for both fuel and reaction mass, and icy moons may work well for replacing water.

I'm not talking about travel. I am talking about permanently living between the stars, and essentially living off hydrogen harvested from the interstellar medium.