Iceland is very safe, the crime rate is one of the lowest in the world.
Three nights would be enough to get an overview of Reykjavik and decide whether or not you like it but nothing more, if you do like it, you'll have barely scratched the surface of Reykjavik let alone the country. We went for 4 nights and came away with a long list of things we wanted to do.
In a short trip in winter, I'd plan for a northern lights tour (book this for your first or second night as if you don't see them, most companies will let you have another trip for free).
Also get a city pass and visit a lot of museums (good if the weather is really awful) and go swimming in the heated outdoor pools if you're feeling brave.
Then just wander around Reykjavik. I liked the pond, the nearby park and the relief map of the country in the City Hall next to the pond.
We found eating out at lunchtime in coffee shops cheaper and better quality than chain coffee shops in the UK. Restaurants were 50/100% more expensive than mid range places in UK cities especially if you had steak, wine or fish.
If I went on my own I'd probably eat out at lunchtime and self cater for breakfast and dinner.
I'd be in 2 minds about the golden circle tour in February as daylight is quite short so I don't know if you'd see it all properly.
They have really good webcams just to see a bit of the country
https://livefromiceland.is/multiview/
Other tip if you drink alcohol is to buy it at arrivals on the way in, as that's the least expensive and most readily available, otherwise its not sold in supermarkets only government off licences which have limited opening hours.