I understand your concern about spending a lot of money getting to the tournament and staying at the tournament with no assurance of getting tickets. I have gone to the Tournament every year since 1990, and I always order my tickets from MSU when I order my season basketball tickets. Normally you would not be taking any chance at all in waiting to get the tickets at the tournament from the losing teams' fans. This year might be different because of the season Kentucky is having, and because the game is not in the Georgia Dome (a larger venue). In the early to mid-nineties the SEC basketball tournament was a sea of blue (Kentucky) and red (Arkansas). Now it mainly is a sea of blue, but the Hogs still have a pretty good crowd. Kentucky fans will be trying to buy most of the tickets for sale at the tournament, and I expect to see people paying a big premium at the site, unlike Tampa and Atlanta where one can get a deal from the fans of losing teams. Beware of the "perfect storm." That would happen if Arkansas and Vanderbilt (the "home team") have good seasons in addition to Kentucky.
Last year I took the entire family to Tampa for spring break, so I needed more tickets than the four I had purchased from MSU. I ordered the extras (for the first game only) from StubHub and paid a premium. However, that allowed me to buy the remaining tickets I needed INSIDE the St. Pete Times Forum rather than having to compete with more ticket buyers outside. When the first game is ending, just head over to the section of the losing team and ask if anyone wants to sell their tournament pack. You are more likely to find the tickets at a reasonable price inside the arena.
As to your question about where to stay, I am staying at the Hilton which is right next to the Sommet Center in Nashville. I reserved my rooms many months ago, and I am paying a premium ($400 per night per room) for the location. There are many acceptable hotels in downtown Nashville, and you can find them on Travelocity, Hotels.com etc. All are a reasonable walk from the Sommet Center.
Don't be discouraged. I am confident you can find tickets and a hotel for the tournament, and I believe your efforts will be rewarded--just as we were rewarded for going to Tampa last year. It is fantastic to compete in and win the SEC Men's basketball tournament!
PS. Edited to say for clarification that when I say I ordered extra tickets from StubHub for the "first game only" I meant, of course, the afternoon session of the first day of the tourament which consists of two games.