The first two sentences have the same meaning. The third sentence is completly different.

Despite this, there is a small subtle difference for the first two sentences.

J’aimerais prendre un café avec vous. -> I would like to drink/have a coffee with you.

Je voudrais prendre un café avec vous. -> I would want to drink/have a coffe with you.

The first sentence is more polite than the second because it expresses the intention : I would like to have a coffee with you, only if you agree. The second one is still polite too, but the feeling could be different, it is a "little" bit stronger (French advanced).

The last one is correct but it means something completly different :

Je voudrais avoir un café avec vous. -> I would want to have my own cafe restaurant with you (building).

The sentence is correct too. But it does not mean what you expect. Since you are not 100% francophone, people will still understand that you want to drink coffe and you will not open a coffe shop.