1. Landmannalaugar

If I had short time in Iceland and would have to pick one trip to the highland I would choose to go to Landmannalaugar on a day-trip by bus. It is a day you will never forget. The nature is very colorful, you see new colors just by turning your head, and if you take a short walk you can have a look at some hot springs. Don't forget your swimming suits and bathe in the hot river. The river runs over a hot area and get heated by that.
The road is not 'very bad' but not suited for small cars. Just before entering Landmannalaugar there is a river to cross, only for bigger cars. Some people leave their car on the other side and walk the last part, it only takes 10-15 minutes to walk from there to the main facilities. There are scheduled trips from Reykjavik to Landmannalaugar. Check for example this website.
Remember to bring food, sleeping bag and other equipment as there is only small café located in an old bus, but no other shops or restaurants. The cabin is owned by 'Ferðafélag Íslands' (a society for hikers). There you can by acocommodation and use their facilities. It is also possible to bring your own tent and camp on the lawn (or on the sand).
About 2-3 hours drive from Reykjavik.