「タッタッタ」って車に乗ってみたいな。
I'd translate the sentence like this:
I want to enter/ride in a car that makes 'tatata'.
I don't think it's the colloquial version of ような, so I think it is みたい plus な. But in this case, I don't know what it supposes to mean.
What is this な at the end?
This な is different from な used in orders (e.g. 行きな or 行くな) and is usually considered to be a stronger/masculine version of ね (but with a more wishful nuance). Sometimes it also occurs in the emphasized version なあ, similar to ねえ.
Probably the most used expression with it is いいな(あ), expressing envy over something which happened to someone else but you'd like to experience yourself.
See also answers to Identifying different ending -な s
Here な is one of those emotive particles that can get tagged to the end of a sentence. I'm not entirely sure what the 「タッタッタ」 part is about, but otherwise the sentence is saying, kind of dreamily and hopefully, "I'd like to try a ride in the car". If you were to try to translate な directly, then you could add something like, "wouldn't it be nice if..." but I feel that's really stretching it a bit and such a translation won't necessarily work universally. (I guess I already tried to get part of that feel in my translation when I wrote "I'd like to try" instead of more directly "I want to try".)
As A.Ellett said this な shows the speaker's desire. It's the kind of thing we would use emphasis words or vocal inflection to denote in English. You can hear girly girls lengthen and often nasalize this, which can be represented as な～ or なあ. By the by, a "cool guy/girl" type (or even someone being snotty) would use this inflection みたいな{LHLL}, whereas みたいな{LHLHH} is more endearing and effeminate with or without the ending あ.
As for the 「タッタッタ」, it immediately makes me think of the Flintstone's car because タッタッタッ is the sound of jogging or trotting. It's more rhythmic than a full sprint sound. More likely it's meant to imitate the sound of a vehicle with a large muffler or something like that. Think the sounds we use in English for a train chugging along.
Also, Igor Skochinsky's explanation for いいなあ is the best I've ever heard. You can hear this a lot among school-aged kids.
Your translation is fine. If you want to represent the な, you could change it to
I really want to ride in a car that makes "ta-ta-ta."
or, more colloquially,
I'd really like to ride in a "ta-ta-ta" car, you know?
Also, keep in mind that みたい adds the sense of "try" or "try out" to the sentence, so maybe the most natural translation would be
I'd really like to try riding in one of those "ta-ta-ta" cars, you know?
