"At what time would you like to meet?"

"At what time would you like to meet?"
 

Would it be:

A que hora querrías encontrarnos?

Or is 'preferir' better?

A que hora prefieres encontrarnos?

Also, is 'encontrarnos' or 'vernos' better?

Don't forget to use the 'Accents' drop-down menu that appears just above where you type. That's what I use to insert all the special characters needed when typing in Spanish. :) ¿A qué hora ...

The 'would' in the English question is there for politeness. Therefore, the verb in Spanish doesn't need to be conjugated in the conditional mood.
You can ask the question using the present tense. This will mean 'in the near future'. This is possible in Spanish, but the English present tense cannot be used to mean the near future.

It can be as simple as:
¿A qué hora nos vemos?
¿A qué hora nos encontramos?
¿A qué hora quedamos?

You can throw in a proper-to-person conjugated form of querer, desear, gustar or preferir to add the 'requesting your opinion' feel. You can use the infinitive to avoid the use of a noun clause cast in the subjunctive mood.

¿A qué hora prefieres que nos veamos?