So, we hopped on the train, and as promised arrived in Milford in ten minutes. As we got off the train we heard gunshots. Turns out it was the Milford Memorial Day parade, and we all know Americans cannot have a parade without firing off guns as often as possible. We went down to where the parade was on the assumption that it was likely to be the centre of town, and therefore probably a good place to catch a bus.
Parade-watching Americans:
After watching the parade for a while, we asked a nearby woman how to get to the state park.
Woman: "Park?"
Helena: "Yes, there is a State Park in Milford?"
Woman: "Oh, the State Park. You can't walk there."
H: "Yes, ok, but we were told there's a bus...?"
W: "No, it's way too far. If you want water, you can go down to the harbour. Why don't you just go down to the harbour and then you can watch the rich people on their boats!"
Awesome. Very helpful. However, we thought maybe there might be something to see down by the harbour, so we headed down. But all we saw were rich people on their boats (and not even sailing - they had literally pulled lawnchairs up to their boats and were sitting beside their boats, drinking).
Then Helena spotted a Bird Sanctuary sign. Perfect! That would do nicely for a little walk and maybe a nice place to sit. There was a little road going in beside the giant Bird Sanctuary sign, and so we followed it into the trees.
Five minutes later we were looking at houses.
The "bird sanctuary" was about twenty metres deep, with a suburb on the far side.
Huh. America, hey? So, we headed back toward the harbour and stopped at a marina and asked a man sitting there how to find the beach.
Man: "Beach?"
Me: "Yes, we heard there is a beach near here. Maybe at the State Park?"
Man: "Oh, that's too far to walk."
Me: "Yes, THANK YOU, but apparently there is a bus."
Man: "Bus?"
Me: "A bus to the beach?"
Man: "Oh, the SHORE bus."
Me: "Yes! Probably the shore bus."
Man: "I think there is a bus stop somewhere in town." [sends us back exactly the way we came]
So, we trudged back to the centre of town and saw the original woman again. "Oh hi! Did you find the harbour? I could give you a ride to the park, but I won't because then you'd have to hitch-hike back, ha ha! Bye!"
Awesome.
We didn't have a map (mistake!) but Helena remembered roughly the layout of the town and the direction of the park. She said it didn't look too far, and we were assuming that an American idea of "too far to walk" might differ from ours. So we started walking toward the park. It was boiling hot and uphill, and after a while Helena mentioned that on the map she saw, it looked like there were beaches BETWEEN the town centre and the park. So we took a sharp left in the direction they should be and kept walking.
Eventually we came across a man gardening. Helena stopped to ask directions.
H: "Hi, could you tell us how to find the beach?"
Man (strong non-American accent): "Yes, keep going straight for about another half a mile. At the end of this road you'll see the beach, but you have to go between the houses to get to it."
Directions! Actual directions!
Moral of the story: if you need to know how to get somewhere, find a non-American.
So, we thanked him profusely and trudged down the road. We were starting to lose faith when we noticed some reeds and other waterplants behind some of the houses. This seemed promising, but we were starting to think we might never find the elusive beach. And then, as we came around a corner - silver sand! There was a sand-covered path between the houses, as promised, and then a glorious silver beach off in both directions.
So, long story short, we found the beach and it was wonderful.
While sitting on the beach, we noticed that all the boats seemed to be going in one place along the shore, and surmised that this must be the harbour. We walked along the beach in its direction, and then cut through the residential area that abutted the shore. After a short walk, we found - the end of the road we were STANDING ON when we asked the first man how to get to the beach. ARGH.
But never mind. We found the beach! And next time, bus or no bus, we can get there the fast way.
Here is a handy map of our adventures:

Legend:
Red X: Talked to man at marina.
Red line: original path
Star: Talked to helpful non-American man
Smiley: Beach!
Blue line: route back to town
Blue dotted line: backtracked to check what we suspected... that the marina where we talked to the first man was just around the corner.
Please note that we were right beside the state park. Non-walkable, my foot.