We had both my DS and DD's first birthday at a local park, both started at 12:30 PM. Both were about 2 hours long. I wanted it to have it at a time when I could invite lots of people and serve a proper meal (lunch). I didn't really worry too much about whether my kids would be on 1 or 2 naps come their birthday parties, only because both kids are easily APOP for an earlier nap if needed.
It was really easy with my DD, because even though she started the 2-1, she still went down for her nap at 11 and we woke her around 12:15 to head out to the party. She had a blast at her party, just "walking" around and showing off her new skill. By 3 PM, when the party had ended, she was exhausted, so we were able to put her down for another nap.
With my DS, it was a little trickier. My brother got married the evening before, so we were out late (past 10 PM) so DS slept in the next day, so no time for an early nap. Then he got fussy around noon while we were setting up. One of my uncles had to walk him around in the stroller until he fell asleep. He slept for a bit, but was awake for his cake and still had time to visit with his guests.