Every tour we sell that stops at Forest Lagoon leaves from Akureyri. Akureyri, where most of them start, is about 5 h 35 min from Reykjavík by road.
4 of the 6 collect you from your accommodation or a designated stop, so the tour is the transport — there is nothing else to arrange and no timetable to read.
A seat on a day tour here starts at €154 and typically runs €161, per person, private charters excluded because those are priced per vehicle and would flatter the figure. There is no scheduled bus we can sell you to Forest Lagoon, so a guided day is the practical way in without a car.
The days themselves run from about 4 h to 6 h door to door, so check the length as carefully as the price — the cheapest seat is often the longest coach day. 4 different operators run here, which matters more without a car than with one: if the weather cancels your day, there is usually another departure rather than a lost trip.
Being driven is the easy answer here: enough operators run it that a cancellation rarely loses you the day, and you get to look out of the window instead of at the road.
Cheapest way in without a car: a guided day tour from Akureyri, from €154 per person.