You can of course walk to the former Eyjafjallajökull eruption site as it is on the Thorsmork -Skogar path, but my understanding is that it is illegal to walk much further off the path to the top of the ice cap as it is a strict reserve. At least that is what it said on the Julia Bradbury TV show about walking from Landm to Sk you can find on youtube. She was taken there in a helicopter after applying for special permission, rarely given.
You do have to walk over a steep snow slope to get to the top of Hekla. And most people don't bother going to the top because there isn't much point in zero visibility and with high winds making it dangerous. It does hide in the clouds most days. Then there is the issue that historically its eruptions have come with only minutes warnings: the met office hopes that with modern instruments they might give an hour's warning, but you'd have to be listening out for it to hear it as soon as it came. Clearly with suitable experience you can do it yourself, I don't think you usually use crampons. Part of the reason that the guided tour is expensive is because of transport to the trailhead is up a very rough track and thus needs a suitable vehicle, the track is about 8km long from the main track the bus takes to Landmannalaugar. You can take the bus to, in practice stay overnight at, Rjupnavellir and walk in but it makes it long walk.
Hvannadalshnjukur is a rather more serious expedition because of the glaciers. Even experienced mountaineers with glacier experience, but without local knowledge, have killed themselves around there. You are perhaps a bit late in the season to find an organised climb. Summer season is generally considered over for more serious stuff by about 20 Aug.
Herdubreid is accessed at Herdubreidarlindir campsite, which is accessible on the Askja tour which operates out of Myvatn, you can also get a connection to the tour at Akureyri. But it is getting late in the season for it. Check the operating dates, but be aware that some years the road is already snowed in by the last week of August. It is a nasty climb due to steep loose material. Someone who appeared to be experienced tried to do it one time I was there, but gave up as he was getting scared with all the material falling down.
It is much easier to climb the mountain at Askja itself, that's just a walk, if you can get there. Some people did it in a storm last time I was there, set off after arriving on the bus and didn't come back till midnight. We flattened their tent and put rocks on it so it didn't blow away or get smashed to pieces, unlike some other tents.
There are of course hundreds of more modest mountains you could climb, just look at the map.
