Here's my eeek!!!
If you have an outdoor facility or one set aside for such use, that would be well and good. Otherwise your building needs to be structured for rentals so far as food service, restriction from galleries and collection areas, etc.  I'd look at Denver Art Museum's policy for food & flowers & rentals if I were going to do this.
I suppose birthday parties are more benign than alternative activities that I think of in regard to "not-mission-related" use of facilities. But birthday parties bring to mind gooey, crumbly cake and drippy ice cream, lighted candles and other problematic items. (screaming children, rauctious (sp) adults...)

When facility rental came up and we were not equipped to handle it (poor configuration, insistence on exhibits throughout the building, no kitchen) I was tempted to suggest outrageous fees.  If you look carefully at your cost (cleaning - you will do it you will not farm this out) staffing, utilities  you will find that you won't be offering an inexpensive rental even if you want to just break even. 
I'd also suggest limiting the number of events you schedule.  How many nights does your staff want to work late?  How many hours can you afford to have them take away from more directly mission related activities?
 
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