It doesn't work. I enjoyed the first episode, but it went downhill after that. It's a buddy comedy that's not funny. It doesn't hit the depths of unfunny, but it almost never made me laugh and I never cared about our heroes' misadventures. It's based on a 19th century Japanese road trip comic novel, called Toukaidouchuu Hizakurige. Apparently, the anime's English dub is funnier than the original, but I watched the latter anyway. Its picaresque anti-heroes are:
1. Robby Yarge, a woman-chasing serial loser who's on the run from the mob. He keeps borrowing from them to fund his get-rich-quick schemes. This should have been funny, but Robby generally comes across as a generic mildly lowlife goofball rather than as the human disaster area you'd expect from that character description.
2. Hatchi Kita, a privileged young man in white who's on the run from his boring life. He's excited by anything new. This can be mildly amusing, e.g. in ep.7 on the theme park planet where being grumbling is against the law. While his more cynical companions are getting glared at for social infringements, Hatchi thinks it's great and wants to stand in line for everything.
3. Their robot, who shouts at them a lot.
"SPACE: THE FINAL TOURIST SPOT" says the title sequence, which sums up the show's problems. Our anti-heroes are bumbling from planet to planet, but in an episodic, inconsequential way. Sometimes they help the people they meet, but it's all too silly and trivial for you to care about those guest stars either. There isn't a plot. Even the mob enforcers are chasing Robby because their gay, gorgeous leader has a crush on him and nothing bad's going to happen there. (That gang boss, Yang, is the nearest the show has to an interesting character, actually.)
That's what kills the comedy. Take the ep.4 scene where a giant robot's filling up with water. That should be funny, but it's not because Robby and Hatchi don't sell the laughs. The scene's dramatic weight is indistinguishable from all the show's other scenes, thanks to our heroes' loud, bland reactions.
The ideas and design work are colourful. Robby's spaceship can turn into a giant robot, while each planet is cartoonishly themed. There's a robot-ruled planet where humans are seen as nobodies. There's an octopus planet, a kappa planet and a giant eel planet populated by half-naked musclemen. (I think the show's aimed at fangirls, incidentally, with an all-male main cast and the occasional bath-towel scene.)
I don't hate this show. It's light, good-humoured and an antidote to grimy, po-faced dystopian SF futures. For me, though, it's a big pile of None Of This Matters. I wasn't engaged and I didn't care, while furthermore (and more importantly) it isn't funny. I'd find it a slight ordeal to be forced to watch another episode without access to a fast-forward button.