There is no real "best place to stay downtown for the price" as it all depends on the person. What one person likes another might hate. It basically depends on what your expectations are, what you want in a hotel and how much you want to pay, time of year, etc. very subjective as we all have different perceptions and wants in the hotel. you don't give much info in what you want/expect in a hotel so it's hard to really say which would be the best for you.
GN is probably the best place downtown to stay but more pricey too so it depends if you are willing to pay more (probably double other hotel rates) for a nicer place. The el cortez generally has the lowest rates on web sites much of the time but for this summer the vegas club has weekday rates that are less than $20 which includes all taxes and fees. The spike also has some low rates but beware of their resort fee. The el cortez rooms in the tower are roomy and decent but some people don't like the walk as it isn't under the FSE canopy. Even though the vegas club rates are low some don't like the (old and worn) rooms, slow elevators and general atmosphere of the casino. From other posters it does seem that the odds on the machines are somewhat better at the vegas club lately.
All the downtown hotels have pluses and minuses so it all depends on what you are looking for in a hotel casino. Some like me are price conscious and are willing to stay at a 1 star hotel, others rather pay more for a better quality hotel.