First up, I want to point out that Ally Spirits don't have to hang out in the Material world at all. When the master is asleep, or whatever, they can just go to their own native metaplane. So my first response to the "what do ally spirits do in their free time?" is: Spirit Stuff! back in their own realm. Its like asking what the Genie was doing in the lamp for those millenia. Or what that Barbed Devil in D&D was doing before you cast the calling spell.
But, lets go ahead and presume that the Ally spirit is going to stick around in the material world most of the time (for whatever reason):
The only rule that points to Ally spirits staying close to the master is the first line of Ally Spirit Abilities on page 201: "Ally spirits follow standard rules, with the following exceptions:"
None of the exceptions mention lifting the standard spirit range limitation. Spirit Range has its own heading in the Core Rulebook on page 302:
Your spirit can’t move farther away from you than your Magic rating x 100 meters. If forced out of this radius, the spirit will try to return as quickly as possible. If you send a spirit beyond this range, it counts as a remote service.
So, yes, an ally can be sent beyond the standard range, counting as a remote service (of which it has an unlimited amount). But following the standard rules for spirits tells us that the Ally won't
want to leave that range if it can help it. Yeah, spirits are their own sapient beings, but remember that Ally spirits are literally created from scratch (usually by the master). Their entire existence is formulated ahead of time by the master. The Street Grimoire goes out of its way to reiterate several times how loyal allies are to their master (at least to start with), even going so far as to call them out as "like a lost puppy willing to do anything for its master" (SG, pg 190).
Not saying they can't (or don't) develop their own personalities, quirks, preferences, interests, etc. Just that their entire world starts out centered around their existence purely for and by the sake of its master. This heavily influences the spirit and what it might want to do. At least initially, an ally spirit probably wouldn't even think about straying far from its master, why would it want to? It has an ingrained need to stay close (Spirit Range).
So while I understand the idea of letting your ally spirit do what it wants and let them develop their own 'character' remember that they aren't people. Sapient, yes; but humanoid, no. They are creatures native to a different plane of existence, they have a whole different set of priorities, and Allies are initially programmed to put their Master at the top of that list.