Honestly, you have the gist. We were just there this summer, and here are a few additional takeaways:
UPON ARRIVAL:
Send one person to pick up the rental car while the other waits for the luggage. The line for the rental cars is short until it suddenly isn't. Being first out helps.
FOOD:
Food is expensive if you are eating out, but for islands, it's quite reasonable to go to a grocery store. We booked places where cooking was an option and ate a lot of sandwiches on the road. Apples, yoghurt, etc. made for a healthy trip, and we were always prepared when we realised that things were smaller than we expected and there was nowhere to eat. The absolute surprise gem of eating out was Muntra in Fuglafjordur, but we also liked Cafe Pollastova in Sorvagur. Like in many places, grocery stores are closed on Sundays. Alcohol sales are quite strict--only liquor stores can sell alcohol in a closed container, and a restaurant has to open your beer before they serve it to you. For traditional food (and we learned this on our last day, so we didn't get to try it), there is a food truck called Streetfood Foroya that is affordable and serves the fermented meat at an affordable price. The trick is knowing where it is as it is mobile. But they do have social media.
PUFFINS:
Obviously for puffins one goes to Mykines. However, should your trip not take you there to see the puffins, don't fret! There are two places we found great for the puffins, and both are worth a visit on their own merits: Gjogv and Mullafossur / Gasaladur. However, do the Vestmanna Seacliffs puffin tour anyway because the cliffs are Just. So. Impressive. From Sorvagur we did a boat tour that we loved. It seemed a bit casual at first, but we learned a ton about the other birds of the island, saw waterfalls that can only be seen from the water, and found our guide was the most amazing local font of information imaginable. Very worth it, even if his initial approach had us questioning whether we had picked the right boat trip. Turns out, we did.
FLOATING LAKE:
Check your weather report and time your hike carefully The weather report said there was to be a break in the clouds and rain around 11 am. The hike is about an hour. We reached the view spot shortly before 11 in whiteout conditions. Sat and had lunch in the misting rain. By 11:20, the weather had cleared, and we had the expected 45 min or so of views. Then it was fogged in again by the time we got back to the bottom. The hike is not at all hard for anyone who is moderately mobile, with only the very last bit a tiny bit steep--but they were working on that trail section while we were there. The trail was quite well maintained otherwise. Trail maintenance varied, by the way.
TUNNELS:
The main tunnels--between Vagar and Streymoy, between Streymoy and Eysturoy, and between Eysturoy and Bordoy--require tolls. Plan your trip so you aren't bouncing back and forth through the tunnels, but be sure to go through the underwater roundabout at least once. Want to travel between Streymoy and Eysturoy? Use the bridge near Oyrarbakki.
Be sure to:
--Pop into the tourist info center at Torshavn to get good brochures and maps, find out about specialty tours and get assistance with bookings, etc. We did a beer tour in Torshavn (only weekly) and toured the brewery in Klaksvik
--At Saksun, walk down to the beach and along the inlet down to the water
--At Tjornuvik, play with the dog if he's there (he's been there for at least 9 years tricking tourists into throwing kelp for him, so I don't know how old he is, but he seemed fit enough).
--Make a reservation for the ferry to Kalsoy or you risk not getting on. At least not with a car.
--Visit Vidareidi!
--Don't assume the weather is bad (or good) on the other side of a ridge. You can be fine and suddenly be driving in heavy fog or vice versa. Just because it's foggy, don't assume you have to cancel your plans, either.