hypothesis testing dependent proportions /repeated mesurements proportions

I need statistical advice:

I have two groups, e.g. young (N=57) and old adults (N=61), and 4 sights in a city. The task for all participants was to visit either one, two, three or all four sights in the city.

The result is a frequency table of how many participants visited the four sites.

       Sight 1      Sight 2         Sight 3         Sight 4
Old     80%         45%             33%             45%
Young   78%         60%             30%             42%

I would like to test 1) sights were visited in similar proportions across the participant groups and 2) whether the proportion of participants visiting each sight was higher/lower in old people.

Looking at the table, I would expect that the sights visited are equally distributed across the groups meaning that Sight 1 has been visited by both groups more than Sights 2-4. Also I would expect that the proportion of young people that visted sight 2 is higher compared to old people. How would I test this?

I thought about a chi-square test but the as the participants can visit one or more sights the sample is not independent, this test seems not appropriate. Also, I would like to avoid the multiple testing problem as much as possible.

Thanks