I think Rekyavik will be your only option for flights if you're going from the UK.
It's colder than the UK all year round so depends if you want a winter holiday (when you'd need really good outdoor clothing) or summer (but except days that are colder than a UK summer). We went in August and had some lovely sunshine, it was pretty dry but we wore jeans and t-shirt with a jumper or jacket to hand sort of attire.
What to do.....whatever you want! Get a guide book a read up, there's some pretty standard tourist trails such as the golden circle. If you don't want to join a tour group then you'd probably need to hire a car but the roads were good and we found driving easy.
It is eye wateringly expensive, don't underestimate how much it will cost!! We did AirBnB / VRBO properties so saved money on food by self catering and taking some bits of food in our luggage. The supermarkets were full of tourists doing currency conversions and declaring "is that really correct??"!

We went In January and it was cold but was really beautiful.

We obviously did a northern lights trip, the blue lagoon and saw some of the waterfalls.

One thing I really loved was a husky trip we did. That was lots of fun. We also did a glacier walk but o wasn’t so bothered by that.

We also had a lovely time walking around Reykjavik, seeing the cathedral, at the rotating restaurant and having a seafood buffet as a cheap place in the harbour.

Food is expensive though..even things like cereal!
We stayed in an apartment and ate in a bit and out a bit.

Oh we didn’t drive because we went in winter. Having see what’s the roads looks liked when we going on some of the excursions I wouldn’t want to drive there myself in winter.

Driving is easy, but very boring! Speed limits are very slow, speeding fines are very high, and the roads are very inviting to whizz on!

If you self drive and like a walk then this is a lovely spot, about 45min walk from this point up to a wonderful hot spring where you can bathe in the river.

Reykjadalur Hot Spring Thermal River
maps.app.goo.gl/ixH7sUohZ4u2fUgG6

I am from Iceland.

For the driving part first, maximum speed is 90k and the police is quite strict on this. The roads can be quite narrow in places.

It’s going to be expensive whatever you do as an activity or shop for food.

Restaurants are great over there.

The golden cycle is nice. But do go to grindavik to see the lava from the newest volcano eruption. It’s beautiful but do pack food with you and stay safe and warm.

Summer holidays are amazing with 24 hour daylight during this time, saying that Christmas is breathtakingly beautiful too.

Get the hot dogs from the popular Reykjavik harbour place and Tomma borgarar is a must for burgers if you like some quick food with quality and taste.

The locals are friendly.

Try the blue lagoon in Grindavik, quite expensive but great and very popular.

Midnight walks during summer is amazing

Message me if you want some further information