Get out of the area that you live in.  Hobbying in public in your hometown or in an area where you know a lot of people is a bad idea.

If you aren't married than any explanation will suffice.

I have taken ladies out for lunches and dinners and always know that there is a risk of bumping into a "friend or relative".  But I have always approached this dilemma that I would introduce my gal pal as a tax client (and in some cases they actually are as well).  And ironically enough I have quite a few "real clients" that I go out with, that some might also raise an eyebrow to.

If you are confronted with that dilemma, stick to the "story" and don't flinch.

Or you could be like Ari Gold (Entourage) and just not "fuck em"

OK, I already used that one recently.

Basically, no matter what explanation you give, you're screwed.  People will tell just from your manner.

So take the advice of others and don't be caught out in public anywhere near where people you know might see you.

That or dine someplace where the lighting is so dark, no one can see you, or a place with private booths.

I fix computers for friends all the time,  sometimes for free. So I am her computer guy and she is repaying me with dinner.
Just keep it simple and somewhat plausible. I have run into co-workers in the past with ladies that are not their wives. All I needed was a somewhat plausible story in case someone else asked.

Lots of excuses could work (cousin out of town, old coworker from a previous company, real estate agent)

Like Mr Fisher has said it's much easier if you don't take her to dinner.

Lots of excuses that can work, just keep them simple and believable

If you are married or have a SO you are inviting trouble.