Your sentences (mostly) have the same general meaning of the car being near the garage, but the choice of word does have nuances that will determine the flavor of that nearness.
- そば says specifically that it is next to, or beside, the garage.
- よこ emphasizes that it is horizontally next to the garage, as its counterpart is たて. Basically using this can be alternately phrased as "not たて."
- ところ is much more vague. You're saying the car is in the same place as the garage.
- ちかく is like a half way point between そば and ところ in terms
of distance with regard to an unspecified location. You're saying
it's near the garage somewhere.
- となり has a generally equivalent meaning of "neighboring" even here, and has an image similar to よこ and そば. As you know it's usually used with houses or the like.
So as you can see it's not exactly true that that they all have the same meaning. They all convey the same general idea, but nuances still have an effect. The more general a word is, like そば or ちかく, the less you will invoke potentially unexpected nuances.