Tagg Romney should definitely run for Senate. It will be funny to see him struggle to juggle the Republican values and trying to distance himself from his father. I don't believe he has any shot of winning any election, but I do think it would be rather fun to see him try.
There is no good reason for Tagg Romney to attempt to hold the office of Senator in the United States. The American voters have already shown that they do not like Mitt Romney or the rest of his family. It is hard to imagine that Tagg Romney has any chance of winning.
If he were to run for Senate, I don't think Tagg Romney would be successful following Mitt Romney's massive loss for the presidential bid. Obviously, people were not impressed with the Romney beliefs, so running so soon would just look like a way to get back in the news and I don't think he would be taken seriously.
The Romney family is somewhat of a joke to the American public. They are this super rich family who is completely out of touch with the average folk, and the things that come out of their mouths are just ridiculous. Tagg Romney would only continue this legacy if he tried to run for public office.