Hi , I will be spending 24 hours in Reykjavik next week. Any suggestion what is the best way to travel between the airport and city.also any must see/do? Thanks

Blue lagoon is a must.

to add on. Shuttle will take you from airport to blue lagoon then to town centre (or vice versa). Blue lagoon is opposite of town centre so it makes the most sense to do it leaving the airport or on the way to the airport

Aeran After Hallgrimskirkja walk down to the water to see the famous Sea Voyageur statue, then over to Harpa concert hall (gorgeous reflecting glass structure). From there, check out an array of dining. We really enjoyed the "fry pan dinner" of cod or Arctic char at Messin.

Val I second this had a great meal at Messin while over there pop in to Kex for a drink

Yes to blue lagoon and tons of seafood restaurants. Enjoy

https://www.dineout.is/fridheimar?isolation=true&lng=en
DINEOUT.IS
Friðheimar

This tomato place was a real highlight for us!

Ken Mulhall
Golden Triangle tour

I took an airport shuttle . Also you must go to Blue Lagoon. Do a bus tour and see a gyser

Enjoy the midnight sun

I used Gray Line bus tours to arrange a shuttle to town. (I was on a tight deadline.) but tehy can take you straight to Blue Lagoon too. And arrange with them a public ride back from Blue Lagoon to town, about 3-4 hours later

I rented a car but in hindsight the bus would have been better

Go up in the Hallgrims church fir a great view
https://visitreykjavik.is/service/hallgrimskirkja-church
Across the street is Loki cafe serving an amazing rye bread ice cream
VISITREYKJAVIK.IS
Hallgrímskirkja church

Just chiming in to also endorse blue lagoon. I try and avoid “tourist traps” like the plague but this was truly a highlight of iceland for me.
In 24 hours you can also do the entire golden circle as well. I’d highly recommend doing this either via bus tour or rental car. I think renting a car will be easiest as you can do everything on your own schedule.

+ Blue Lagoon
+ Big church in city
+ Golden Circle
++ Rent a car so you can do everything on your own schedule.
I’ve been there 3 times now, such a gorgeous country.

Also the walking tours are great, great guides and information about the city - 24 hrs is not enough you will wish you had a few more days
Have a great time

You can book to blue lagoon its beautiful

The sea Barron