Q:

What upkeep is needed to run buildings and organizations?

The Downtime Rules from Ultimate Campaign include rules for running buildings and organizations during downtime. One of the phases is the upkeep phase, which reads:

Phase 1—Upkeep: Pay costs associated with maintaining completed buildings and organizations.
...
Step 1—Add Up Costs: These costs include ongoing or recurring costs for your buildings, organizations, and other previous downtime activities that have accrued since the last time you have had a downtime session. Most of these costs are incurred daily, whether or not you are spending downtime days at the settlement.

However, I don't see anywhere that describes what the recurring cost of a building or organization may be, besides hiring a manager. If one does not hire a manager, is there any other recurring gold upkeep required to maintain a building or organization?

A:

Not exactly. The upkeep referred to is the cost of that building's earnings. For example, let's say you have an alchemy lab, and you're gone for 5 days. If you told the lab to earn magic for those 5 days and take 10, it earns 10 magic. This results in an upkeep cost of 500g (the cost of earning 10 magic). This, in addition to your managers, is what upkeep refers to.
So, if your building is just sitting idle and empty, there is no upkeep associated with it.

A:

No, it's just a confusing buggy rules system.  Upkeep costs are not defined for buildings or organizations.  See this Paizo thread for all the other confused folks wondering about this and hoping they'll errata the whole system at some point. 

