The problem isn't around, actually. It's your use of the roads. When you "travel around a city" by scooter, it's taken as given you will travel on the roads. After all, scooters aren't good for traveling anywhere else. It might have been better to write:
A lot of backpacking guides recommend renting a scooter to travel around the city.
This is pretty clear. You rent the scooter to travel to various locations. It's not specific whether those are within or outside the city, because that's not really important.
If you instead specify "roads around the city" then we aren't sure if you meant to say the roads in the areas around (outside) the city, or all the roads in that area. In other words, we aren't sure if you are talking about a specific set of roads, or if you simply misused the common idiom.
As an example of the other use:
When traveling on the roads around the city be aware that they are not as well maintained and may not even be paved. Drive cautiously, looking out for potholes and other hazards.
In this second case, it's probably better to use outside or surrounding the city, to make it clear which roads you mean.