Don't go to Barbara's .. it's gone downhill .. Went there about a year ago and it was so dreadful.... (and in my opinion) not the cleanest place in town.. Had the Salmon .. and it was the worst ever.. I am from the Bay Area, so I know good (and in that case) bad seafood when I have it...... BLAH........
There is the Princeton Seafood Company and they have a little window where you can grab an ice cream and walk the beach path. it goes on for a long time.. good for walking, biking , scooters... it's basically flat for the most part.. IF you decide to walk the trail, wear layer clothing. it's deceiving... it can appear all foggy but once it burns off, the trail can get downright hot.. wear sunscreen..
Personally, I would consider packing a lunch and taking it to the beach..
However, Sam's Chowder House isn't bad in the sense that IF you were to order fish, it would be fresh... The desserts (in particular the Key Lime Pie) was pretty good.. It's very pricey though and might be rather busy on a Father's Day (check online reservations) .. IF you do go there.. try and eat in the MAIN room.. the back room didn't feel as fun.. (esp if they have live music) you can't hear it too well back there... I call that part of the restaurant, the forgotten room............ :)
About downtown HMB........... ummm. very cute.. my cousin (and not my opinion) says the pizza restaurant, It's Italia is good..... she eats out a lot.. not sure I agree.. but so as not to be too biased :)
Mostly we go down there to walk the beach path , grab a coffee at the little cafe located on part of the trail and then come back to the city and grab a burrito (La Cornetta) on Mission Street between 23 and 24th.... that's our favorite place..
good luck and have fun!!