We will likely be able to travel anywhere in space we wish to go. If you think of how technology in general has advaced over the last century or even over the last decade, you'll get a glimpse into what is coming next. We can't imagine it now but it will happen.
At first it will be limited to those of means but soon it will be like flying to another country in an airplane. Space travel is already becoming accessible so that just tells you that bigger and better is on the horizon.
It may be possible to travel to Mars and beyond, as far as technical capability is concerned: so much has been achieved in space travel in the last 70 years. We are now at the point where paying passengers can be transported to the moon. As to the rest of the Cosmos, it is not just the technical feat but whether it is possible to survive entirely: physically, mentally, and emotionally, that is the question.
Stephen Hawking believed there must be intelligent life in other parts of the Cosmos. These may seek to hinder any exploration of the territory, including space territory near to them. Such long-distance travel incurs the risk of space radiation. There is already evidence of cognitive damage to astronauts who have achieved lunar tourism. The psychological effects of extended incarceration in a space vehicle and subjection to the fellow passenger(s) is little known, although studies will have been made, I am sure.