I'll give my advice, based on my attending the tournament for the last 29 years..... The Red Lion is actually a pretty good choice. It had several other names in past years such as the Sheraton, and City Center Hotel.
It is the closest hotel to the Enterprise Center, it is literally right across the street from the entrance. However, there are not many good parking options. We have stayed there in the past, and although there is some street parking available a couple blocks away to the north of the Enterprise center (electronic metered parking along Market St. and farther north with maximum 2-hour limit and $1.50 to $2.00 per hour). However, it is somewhat limited, and that area also has a significant car theft and break-in problem. See this recent article-
https://www.ksdk.com/article/news/cr...1-37d5c3ec1941
Plus, almost every year when we are down for the tournament, I have seen parking patrol officers looking for cars to ticket at those metered street spots. That can negate any savings you might get with a street spot. And, you have to walk a couple blocks to and from the hotel. There are also a couple private parking lots, but they aren't any cheaper than the hotel valet option, plus you won't have in-and-out privileges.
My suggestion is to bite the bullet and pay for the self-parking or valet parking option at the hotel. Just ask the front desk or tell the valet when you pull up. It used to be $25 per night for self-parking, but we stayed there this past October for a concert at Enterprise Center, and used the valet, which was $34 per night. But they park your car in a secure covered garage, and you have in-and-out privileges, which is nice for when you go out to dinner, since there aren't any nice restaurants near the hotel. And because you are right next to the arena, you don't have to look for additional parking when you go to the games, like the rest of the fans do who stay at the downtown hotels.
If you do prefer to try the metered street parking, I'd suggest downloading the ParkMobile app. They have kiosks along the streets to manually pay (2-hour limit), but St. Louis parking meters also use the ParkMobile app for payment. It allows you to add more parking time from anywhere (it still allows only 2 hours at a time) so you don't have to run back out to the car when your time expires.
Info-
https://www.stlouis-mo.gov/governmen...parkmobile.cfm
ParkMobile app-
https://parkmobile.io/
Good luck!