I visited this WHS in 2022 as a very early rise and shine visit (since I couldn't sleep much due to sun almost never going down in the summer months in Iceland). The WHS proper within the Thingvellir National Park is always open 24/7 and parking (any time) in most of the car parks comes with a fee payable by credit card in one of the machines. I parked just next to the visitor centre (still closed when I arrived and eventually left), and in front of it is a very nice viewing platform as well as the UNESCO WHS inscription plaque.

The only really OUV (arguably more of a national value really) lies in the "story" related to the Lögberg”, the rocky outcrop marked with a white  flagpost (the Iceland flag is only flown during the visitor centre's opening hours) where the Speaker of Parliament had his seat and from where public speeches were held. If truth be told this current location might not even be the exact location after all due to changes in the surrounding landscape. In my opinion this should really be extended to a mixed site to cover the interesting natural features of the national park which are by far more tangible than the current WHS as it stands. 

From the visitor centre I followed two main signposted hikes, mainly on wooden boardwalks, which are worth doing, namely the hike to the Öxarárfoss waterfall and further beyond if you are not pressed for time, and the hike down to the wooden church by the water and straight ahead to the Silfra fissure where you can also swim and dive between two major tectonic plates. After a bit of birdwatching, since it was still very early, I headed back to my car to fetch my drone and I spotted someone else coming towards me. At such an hour, I was sure it was a WH traveller, and indeed it was Philipp who shares my same 'obsession' of visiting WHS in sunny weather (as much as possible) and this is certainly not a given in Iceland.