My museum has an interesting situation in that we are free nine months
out of the year.  We bring in a larger traveling exhibit during the
summer months and use an admission fee to help cover the cost while it
is on display.  We have two interactive donation boxes which are out
year round.  There is very little difference in the income from these
whether we are charging admission or not.  From my experience donation
boxes generate very little money, although every little bit helps.  If
you don't need the money from admissions then eliminate the charge.  But
don't count on donations providing the same amount.
If you want greater attendance try other ways such as free days, etc.
The Exploratorium has a policy to allow children in free if they come by
themselves and do not have enough money to get in.  Provide school
children with free passes.  Etc.

Greg Shuman
Exhibits Director
Don Harrington Discovery Center