Wendy Williams is clearly happy to be out and about in the Big Apple ... flashing a big grin for cameras as she went out to dinner amid her guardianship fight.

The former talk show host grabbed a bite to eat at Tucci -- an Italian restaurant in New York City's trendy NoHo neighborhood -- Saturday, arriving in her mobility scooter.

Williams wore a fashionable jacket with blue faux fur trim ... and cherry red lipstick, too.

The dinner marked the end of a long week for Williams ... which kicked off with police arriving at the assisted living facility where Wendy Williams is living before she was taken to a local hospital to determine her mental capacity.

WW passed the tests with flying colors ... and, we spoke to her later in the week about that as well as a judge calling for more restrictions to be put on Wendy.

BTW ... you may remember Wendy went out to dinner with her niece Alex Finnie earlier this week -- and, sources told us the assisted care facility filed a police report over the meal.

Harvey and attorney Mark Geragos have discussed Wendy's situation at length on the "2 Angry Men" podcast ... including chatting with attorney to the stars Joe Tacopina about possibly repping Williams.

Wendy had a wild week ... but, it looks like dinner was just what she needed to decompress!