You'll wish you'd never asked!! This will be our fourth Ring Road trip in 6 years...
I'll try and spell all these places correctly - then you can google them to find out more and exactly where they are. English spellings might miss the accents off their extra vowels and use a p for 'þ' and a d for 'ð'. Also this should all be possible in June/July/August but some things will not be at other times. And I'd only attempt to drive the Ring Road in summer, see Tripadvisor for many dire warnings about winter driving in Iceland.
The 'standard' ring road trip does overnights in/near the following, if you have more days you can add an extra nights at some but this gives up to a 250 km drive between each. Below is anticlockwise but I've done it both ways
Reykjavik/Reykjanes Peninsula (Grindavík, Keflavik)
Golden Circle area (or at the end before Reykjavík)
Vik
Höfn
Egilsstaðir/East Fjords
Myvatn/Akureyri
Blönduós/Hvammstangi
Reykjavík
As well as adding extra days on this route you can do extra days by going off to the Snæfellnes peninsula (needs at least 1 day), Westman Islands (1 day), Tröllaskagi peninsula (1 day or just drive it between Akureyri & Blönduós) or the Westfjords (at least 3 days).
If you hire a 4x4 you can drive on the F-Roads in peak summer (Fjall or Mountain Roads). Even with a 4x4 a lot of these are still not recommended for tourists unless they have experience at things like fording rivers and have a proper Land Rover type vehicle, not just a Dacia Duster. But route 35 is the easiest (no river fording but 180km of teeth rattling track surface) and you can visit Kerlingafjöll/Hveradalir & Hvervellir which have some stunning scenery & hikes. You'd need at least 2 days though and stop overnight (expensive unless camping/dorms).
www.road.is is crucial for driving in Iceland, including if F Roads (or any road) is open. Google maps can be a bit dodgy/inaccurate and add at least a third to any driving times it gives. A local Sat Nav and/or paper maps are good if you are venturing off the main roads.
For Icelandic wildlife below are the main places I know of
Whale watching - Reykjavík (I did this and we saw a few), Húsavík, Stykkishólmur
Puffins - Látrabjarg cliffs in Westfjords (amazing, they were about a metre away and hundreds of them!), also Westman Islands, Borgarfjörður Eystri and various other cliffs have small colonies. If you visit in the evening then the Puffins are less likely to be out at sea and more likely to be on their nests
Seals - if you visit the Seal Centre in Hvammstangi they can tell you where and when you can see seals from the shore around that area. Seal spotting is best at low tide (I think) as they bask on the exposed rocks. I've also seen them off the Snæfellnes (Ytri Tunga) & the Westfjords (near Litlibær)
Arctic Foxes - There is an Arctic Fox Centre in the Westfjords (Súðavík) that has a couple of rescued ones but otherwise it is random. We saw them a couple of times in the Westfjords in the wild and if you go into Hornstranðir (below) you have a good chance as they are not hunted there
Sheep - every-bloody-where! Always be on the look out for them deciding to cross the road in front of you
Reindeer - You might see them between Höfn & Egilsstaðir as they come down from the highlands to nearer the ring road in the summer, I've seen them a couple of times
Horses - Again if you're lucky you might see a huge herd running wild or there are loads of farms to see/ride them
Hiking - this is a tiny selection, mainly easyish walks I've done rather than proper hiking but googling for guided hiking brings loads of companies
The Volcano :) - Close to Grindavík. Seems to change every day but currently it is a few km to view the eruption and nearer to just see the lava field
Skaftafell/Vatnajökull National Park South - On the south coast between Vik & Höfn, various trails, I did one up to a waterfall
Ásbyrgi Canyon/Vatnajökull National Park North - My favourite place, lots of trails around the canyon and others as far down as the Dettifoss waterfall
Around Lake Myvatn - again lots , I've done some round Dimmuborgir
Hornstranðir Nature Reserve - The very top bit of the Westfjords, no permanent inhabitants or roads, only open in the summer. You can get a boat from Ísafjörður and there are various options. We did a half day to Hesteyri which was a few km walk around the 'village' and then coffee & cake but they do full day & multi day hikes right into the reserve
And lastly after all that walking don't bother with the Blue Lagoon - there are several similar spa type places now (Myvatn Nature Baths, GeoSea, Secret Lagoon, Vök Baths, Sky Lagoon) or just go to the local baths, super cheap for Iceland and they all have at least one hot pot and lots are outside. Or find a natural hot pot. Local baths I've used with fantastic views are Patreksfjörður, Þelamörk, Neskaupstaður & Hofsós
Gangi þér vel!