"tramp around" is a perfectly correct and usable phrase in written English.
It can be used to refer to walking aimlessly or expecting to an area without a specific destination. For example, "We decided to tramp around the city until we found something interesting."
This Web site recently wrote about a kind of day camp where people pay money to leave their gadgets behind and tramp around in the woods.
They grab you when you arrive and show you around and tell you everything they want done, and you tramp around for hours and you don't really have a chance of seeing much else.
We tramp around, finding three tombs in the rock, long since emptied of all treasure, much to the disappointment of Maddy, 12. Later that day we drive over a pass and catch sight of Lake Ohrid, 300 metres deep and entirely fed by aquifers.
Nowadays more than 2 million tourists tramp around the monuments every year.
But they missed their sailing date and he was forced, he said, to tramp around the city with his friends.
In the dry season (May to September), up to 2,200 people tramp around the ruins each day.
We tramped around in the snow and felt totally displaced.
As we tramped around, Tuxecan showed itself only as half-buried scraps of rusted metal ("probably associated with a stove," Langdon said) and overgrown furrows ("potato garden").
Most of our customers are out in the open a lot, tramping around, and they mig t just as well be carrying a Sniffer.
In the nineteen-thirties, the stodgy members of the British Alpine Club, accustomed to tramping around on Swiss glaciers with local peasants as guides, used to dismiss the young itinerant Nordwand aspirants as daredevils and glory hounds.
More important, it won Hyde a $7,500 grant from the National Endowment for the Arts, which he lived on for a year and a half as he haunted libraries, tramped around and tried to figure out what he wanted to do next, and how.
