A few thoughts:
- If you are US-based (and possibly even if you're not)...I find National Parks trips are good bets for "unplugging", mostly because wireless service is pretty bad in many areas of many parks. So you can't even use your iPhone to connect to social media even if you want to. I highly recommend Glacier and Yellowstone in Montana/Wyoming area.
- Instead of the Maine Coast rental, I recommend begging, borrowing, or stealing a vintage car and going on a road trip with your BS kid. A long and possibly ill-advised one. I did over 1200 miles with only 7D1 as a navigator (no support truck/trailer) a few years ago and it was an amazing experience for the both of us. You don't know what parent/child bonding is until you are silently and non-so-silently praying to make it across Arizona in 116 degree heat in a vehicle without AC, which may or may not have a small coolant leak you have to stop ever so often to repair, MacGyver-style. Good times.
- Alternately, I recommend that your child take up a semi-esoteric, moderately expensive sport that requires travel throughout the year to convention centers in second-tier cities across the country. The kid generally don't have to miss many days of class (which most private schools are more lenient about than public schools), and you get to bond in the crucible that is elite sports! Again, speaking from experience, these weekend trips are excellent opportunities to bond. As well as build up your reserve of FF/Hotel points.
- I would caution against being too ambitious with any summer plan (at least with regard to duration...the epic car trip mentioned above was only 5 days long). This past summer we did a 2-week trip abroad that was mostly funded/dreamt up by my in-laws and the kids reflected afterwards that while they had a good time...2 weeks was perhaps too much time to be away. My wife and I happened to love the length of the trip (it takes me a few days to forget about work), and were truly surprised that the girls didn't share our enthusiasm. Again, just sharing my own family's experience.
- With regard to "unplugging", I don't think this even requires a cabin on the Maine coast or even a vacation. Instead, simply demand that people (adults and kids) leave their phone elsewhere when doing whatever together as a family. You might get some eye-rolling initially, but in time it will come to be second nature.
- Another suggestion is to institute "Family Game Night" in your household during the times when you are all together. We happen to like Yahtzee and Whoonu.
- Finally (for now), consider using technology as a way to bond throughout the school year as opposed to it being an isolating factor during breaks. We have several different message groups going on FB in our family (various combinations of people) and it's been a great way to stay connected.