Learn Croatian: S jedne strane želim putovati, a s druge strane nemam novca. - On the one hand I want to travel, and on the other I have no money.

You are right that s (or sa) usually means "with" and takes the instrumental case. However, s can also mean "from" or "off of" when paired with the genitive case. In Croatian, you look at things "from" a side, so s jedne strane literally means "from one side".

Could I use i instead of a to connect these two clauses since the English translation says "and"?

No, a is exactly the right conjunction here. Even though English uses "and", you are contrasting two opposing situations (wanting to travel vs. having no money). In Croatian, a is the perfect contrastive conjunction for this, whereas i simply adds similar information together and ali (but) would feel a bit too strong.

Why is it nemam novca (genitive) instead of nemam novac (accusative)?

While you will hear people use the accusative (novac) in everyday speech, using the genitive (novca) is grammatically preferred when dealing with an unspecified quantity (the partitive genitive) or after a negative verb. It implies "I don't have (any) money."

Is it necessary to repeat the word strane in the second half of the sentence?