Mr. Wednesday pays Shadow $4000 a week (apparently, we never see any such exchange) yet they stay in the low-end American Motel (owned by one of the gods?) and Mad Sweeney, Wednesday's ally, also has access to unlimited gold coins.
I can see few reasons:
1. To avoid attention
Please notice that Wednesday is a con man - he has been doing various cons since (at very least) beginning of the XX century: in the book he describes various ways he managed to trick people out of their hard-earned money. If he would start living in expensive hotels full of security, he would attract attention not only of the police but also of the New Gods. Similar would happen if he suddenly start going around trying to convert Sweeney's gold coins into cash - someone might notice and start asking questions and Mr Wednesday likes to keep a low profile.
2. To avoid spending power
Old Gods wane - this is the main theme of the story (it is even said straight in the trailer). Look at the Czernobog: the poor guy is a pensioner living in a shady apartment! Almost no one is outright willing to worship them, they need to use trickery to gain scraps of power. Using it to pull money out of the hat would be a waste.
Please notice how weak the Old Gods are:
- Bilquis was a queen, in episode 8 you can see that she was homeless, living on the streets (in book she is a cheap hooker).
- Zorya Vechernyaya (just like her sisters and Czernobog) is forced to work in the kitchen, when "once she had servants and lived in a palace".
- Djinn (a creature quite often associated with wealth and luxury) is an overworked taxi driver.
- Thot and Anubis work in a small town funeral parlor. In book they complain about fighting a loosing battle with bigger chain parlors.
- Wednesday is severely weakened after healing Shadow. He gains some power back after killing another god (one that had power from regular human sacrifices).
The only god who can have lots of money without much effort is the Mad Sweeney, but he is not too happy with his deal with Wednesday.
On the contrast, the New Gods are doing great - Technical Boy is rich, Media is almost omnipresent. Vulcan - an Old God who changed sides - even says that "They put power back in my hand, and I gotta tell ya, it feels good." source
3. Wednesday is not a "god of wealth", quite contrary:
If you know that Mr Wednesday is really
then you should also know, that he (in mythology) likes to wander around, pretending to be a poor traveler, checking are people following the laws of hospitality and punishing those who are not kind to strangers. Sleeping in five stars hotels would be against his nature - he wants to pretend that he is poor (and actually it is never stated that he really is!) and see how can you react.
In the end, while not rich, Wednesday is comfortable wealthy as shown in the fact that e can afford easily the $4k per week to Shadow.