With millions of dollars at stake in his upcoming divorce, Yankees slugger Alex Rodriguez is keeping a low profile with his romantic life.  By which I mean he's taking various women out for dinners and drinks in different cities.

A-Rod stepped out with a mystery blonde last Wednesday night, starting with a cozy dinner at Dan Marino's [followed by drinks at Bougainvillea] in South Beach… As they got up to leave around 1 a.m., the duo seemed surprised to be greeted by a photographer's flash…

Once spotted, the gallant A-Rod ran across the street, "trying to make out like he wasn't with her," said the source. Realizing that witnesses weren't buying the ploy, Rodriguez said, "This is nothing. She's an old friend of mine. Leave us alone." They then got into his Mercedes and sped off into the Miami night.

What a charmer.  Girls love it when you're terrified to be seen in public them.  Running across the street is almost as good as shoving her into the nearest storefront and putting on a fake mustache.

Back in New York on Sunday night, Rodriguez hit the roof of Soho House with a tall Asian beauty with "good hair," sources report… Just after 11 p.m., his date made her way downstairs, with A-Rod following a few minutes behind her. Then they jumped into a hybrid SUV cab and took off.

Hmmm… tall Asian beauty?  Well, Yao Ming's at the Olympics, so it can't be him.  And he doesn't have good hair.  But what about the Asian's biceps?  Did she have huge guns?  It's not gonna work out unless she can curl 45s.