Getting close to "go time" for you. Wow.
While this is the peak of the tourist season, there should not be any congestion on the roads. Perhaps a lot of people at the sites, but a good deal of folks take tour busses and do not do the drive themselves.
There will be a lot of folks walking up and down the streets in Reykjavik, but that is just part of the summer hussle and bussle.
You should be fine on clothing with something to fend off rain. The temp will be between 40-60, overcast to bright sunshine, no wind to strong (20-25mph) wind, and periods of intermittent rain. Basically, everything.
But it always changes, and in short order. So you can be in the rain, wind, with clouds and 40's and feel cold. The next hour will bring calm, brite sunshine, temps feeling much warmer. Dressing so as to adaptable is a good way to go.
I don't know if you have any maps of Iceland yet, but it looks like you most likely do Thingvellir, Geyser, Gulfoss and head for your stay at Hotel Hela.
Here is a link to the Iceland road commission, with maps of Iceland showing major roads, conditions and such, with yellow boxes that point to sensors they have along the road to report wind and traffic.
This is a link to your first day area, but you can change it by clicking on the map, top left corner:
http://www.vegagerdin.is/english/roa...nd/south1.html
On the left side, you see a lake. The Thingvellir area is at the top of the lake. Then you will probably head for Geyser by taking the road directly east, thru Laugarvatn (nice little town with a fuel station with food), and continue on to Gulfoss. They have a yellow road box labled "Gulfoss" with a connecting line to the area.
From there you might head down Hwy 30, thru Fludir to get to your hotel. Just past Fludir, there is another road to the east, Hwy 32 which goes to Arnes, which is another nice community with a small eating establishment in the communit center. Nice place and we went there when we stayed at that cabin. This whole area is really beautiful.
FYI, the ring road, Hwy 1, leaves from Reykjavik, thru Hveragerti, Selfoss, Hella, down the coast to Vik. Just to give you an idea of your travel the nextday.
If you can, it might be worth it to see Selfoss. It is fairly large...maybe 10,000, with a nice shoping area by the river with a nice path for walking. There is a great little coffee shop across the street, but on the same side as the shopping area (the only big grocery store in the area, if you need something before heading out on the road) and it was nice to sit outside with coffee and pastry/sandwich and watch Iceland pass by.
If you need it, the Iceland wx office link:
http://www.vedur.is/english/
I think you will have a great time.
Wanted to add that the road from just past Thingvellir to just before Laugarvatn (about 20km) is gravel, but this is the only gravel stretch we encountered.