"We stand up from the table and go out to the garden."

Translation: Felállunk az asztaltól és kimegyünk a kertbe.

[guilth]

Would "kerthez" be better?

[vvsey]

No. When you go to the garden, you usually enter the garden, right? That is expressed as "kertbe". If you say "kerthez", you are saying that you end up next to, outside of, the garden.

[Han-Miru]

But the english sentence says "We (...) go out to the garden" so it is not clear wether we actually enter the garden.

[vvsey]

Yes, it may be ambiguous but I think it is usually understood to mean actually entering. Just like going to the street, to your room, to school, to the theatre, etc. Especially considering the fact that, usually, the garden is directly attached to the door that you use to go outside. So your very first step outside would already be in the garden. Most of the time. So, normally, you don't need to say "go out and into the garden".