"Anyway,they want me to go down to this sonogram thing with them tomorrow'
what's the meaning of 'go down 'here?
In this context "go down" is "go down to" or "go to" or "attend". For example;
Anyway, they want me to attend this sonogram thing with them tomorrow.
Here "thing" is not necessary but is sometimes used in casual spoken English.
You should be quite careful with this phrase, as one of it's meanings is of a suggestive nature, in another context, the phrase "to go down" ( you might hear that quite often in hip hop/Rap songs), could refer to oral sex, for example: " she went down on me last night in the car", i would personally recommend non - native English speakers, to avoid using slang words and phrases as much as possible.