'... to meet with...' would suggest a somewhat formal purpose.
"... to meet with the board to discuss finances."
"... to meet with my tenants to arrange payments."
"... to meet with a contractor to fix a date for repairs."
"... to meet with resistance while trying to arrange those payments."
'... to meet...' is usually used to simply describe the act of
coming together, whether for no purpose, or for something informal, and often involving someone, or something, new.
"... to meet for drinks at O'Brians."
"... to meet my blind date this evening."
"... to meet my new girlfriends parents."
There are plenty of exceptions to this, but it's a start.