Uptown Funk is from Ronson's album Uptown Special. "Uptown" is a term used for areas of certain cities, including New York; Mark Ronson spent some time studying in New York and also worked as a DJ there. I'm guessing that that may have been in his mind with the "Uptown" reference. (The video for the song was shot in New York).
Many of the lyrics in this particular song appear to be chosen primarily to fit the music - and Ronson says that this was part of the writing process of the album:
Lots of times, we had a melody already—and sometimes [Grammy-winning producer, Uptown Special co-producer] Jeff [Bhasker] would record a sketch vocal with nonsense words but very specific vowel sounds, because certain melodies work better when they’re sung with certain sounds. This meant that, when Michael came in to write lyrics, his words had to match the number of syllables in our melody and the vowels we had in mind. He just did it. I sometimes felt like we were feeding melodies into a supercomputer that was just spitting back these great, great words.
http://www.theatlantic.com/entertainment/archive/2015/01/mark-ronson-by-heart/384552/
They lyrics as a whole do not tell a story, but if you look at individual lines and sections, they make more sense.
This hit
That ice cold
Michelle Pfeiffer
That white gold
This one, for them hood girls
Them good girls
Straight masterpieces
Stylin', wilin'
Livin’ it up in the city
Got Chucks on with Saint Laurent
Got kiss myself I’m so pretty
This section is talking about looking good, and wearing jewellery and expensive branded shoes. ('Chucks' = training shoes; Saint Laurent = the Yves Saint Laurent brand)
I’m too hot (hot damn)
Called a police and a fireman
I’m too hot (hot damn)
Make a dragon wanna retire man
I’m too hot (hot damn)
Say my name you know who I am
I’m too hot (hot damn)
Am I bad 'bout that money
Break it down
Here he is talking about how "hot" (talented/desirable etc) he is, and how he has a lot of money.
Girls hit your hallelujah
(here, "hitting a hallelujah" is a figure of speech meaning "sing"...)
Saturday night and we in the spot
A "spot" is a night club. So they are at the night club on Saturday night.
So although there's no story to the lyrics, there is a definite theme : being attractive, rich, talented and having an exciting social life.