Learn Spanish (Latin America): No conozco la ciudad y no sé la dirección. - I do not know the city and I do not know the address.

This sentence is a perfect example of the difference between the two verbs for "to know". We use conocer (here, conozco) when we talk about being familiar with a place, person, or thing. You are saying you aren't familiar with the city itself. On the other hand, we use saber (here, sé) for facts, information, or knowing how to do something. An address is a piece of information, so you use saber.

Both conozco and sé look a bit weird. Are they irregular?

Yes, both verbs have an irregular yo (I) form in the present tense. For conocer, instead of "conoco", the "I" form is conozco. For saber, instead of "sabo", it becomes the very short sé. The sé always needs an accent mark so it doesn't get confused with the pronoun se. The other forms for both verbs, like conoces or sabes, follow regular rules.

Does dirección mean "direction" or "address"?

It can actually mean both depending on the context! In this sentence, it usually means "address" (like a street name and house number). But it can also mean "direction" (like left, right, north, or south). Both an address and a direction are pieces of information, which is why we still use saber either way.

Do I need to use the "personal a" after here?