I've spent about 9 months in Iran, and been to most (though not all) areas. What to see really depends on your tastes...
Iran has some of the most interesting and atmospheric of cities in western Asia. Yazd, Esfahan, Shiraz, Tabriz, Kerman, Qazvin, Mashhad and Semnan are all memorable, plus many more.
Iran has a mixed population; visiting Kurdestan, Baluchestan and the northern parts of Golestan province will introduce you to the very warm Kurds, Baluchis and Turkmen, all of who I have found to be especially friendly. There are also many ethnic Arabs living along the Persian Gulf.
Iran has some great coastline. THe Caspian coast is pretty miserable in winter, but the Perisan Gulf is fantastic, with perfect weather; 20 degree days while the rest of the country freezes. The beaches in the southeast (in Baluchistan) are magnificent.
For great rides / drives, Iran has lots. With some preparation you could head across the empty desert wastes following tracks or just heading straight over the desert, though the normal desert preparations and precautions apply. The Police will be rather suspicious of you however as drug smugglers use the deserts to bring heroin out of Afghanistan. The good news is that Iran's huge network of perfect asphalted roads means you can really get 'out there' whilst staying on perfect black-top. Memorable drives for me were:
Kerman - Shahdad (past the Kaluts) and on east to Nehbandan in Sistan. This is a 200km-ish drive through the abiotic Dasht-e Lut, on a new and unused road. It is utter wilderness.
Damghan - Moalleman - Yazd. This is a 500km-ish drive across the heart of the Dasht-e Kavir, the Salt Desert in northern Iran. It passes some old, untouched desert villages, and some very desolate scenery on the way to Yazd, which is my favourite city.
Zahedan - Iranshahr - Beris - Chahrbahar. This drive through the wilds of Baluchistan takes you from high desert through green wadis to tropical coastline. It's not the safest of areas (or so they say), but the people are super-friendly. The beaches around Beris are awesome.
Taybad - Torbat-e Jam - Sarakhs. This takes you through the Afghan and Turkmen borderlands, along the Hari Rud (Tedzhend) River and through some interesting gems of Ghaznavid (Afghan) architecture, such as the wonderful tower at Karat, near Taybad. People here are predominantly Sunni Persians, and Turkmen and are very friendly. If you had a re-entry visa for Iran, you could make the trip to Herat, which is as atmospheric and memorable as any city in Iran.
Bojnurd - Maraveh Tappeh - Bandar-e Turkmen. This takes you along the Turkmen border through an area which is geographically and ethnically part of Central Asia, in the lower reaches of the Kopet Dagh mountains. The landscapes around here are gorgeous, particularly in the north of Golestan province which IMO is the most beautiful in the country.
As for hidden gems, well the country abounds in them, and you'll find your own... but here are a few of my favourites
-the shrine of Khaled Nabi - an un-inspiring shrine of this 6th century Nestorian saint sits above a fairytale landscape of undulating loess hills, and nearby is the truly fascinating Turkmen burial ground which consists of a forest of stone phalli.
-Kuh-e Khajeh - a lost city in the deserts of Sistan, close to Zabol (which is perfectly safe to visit). The nearby castle of Sohrab at Seh-Kuheh is also nice.
-Howraman Valley, Kurdistan. This small valley contains beautiful villages of stone architecture and the Howramani minority of Kurds, who wear very traditional clothing.
-Qeshm Island. Take the super cheap car ferry to Laft, the most original of all Persian Gulf towns.
-Abandoned Silk Road caravanserais and cities. Just driving the lower of the Mashhad - Tehran roads, through Sabzevar, Shahrud, Damghan, Semnan takes you past abandoned relics of the old silk road which are far more atmospheric than anything you'll see in Uzbekistan. Damghan also has some fantastic architecture.
-Tehran. OK, so this is hardly a hidden place, but Tehran's highlights are rather subtle. Hang out with locals, speed wildly on the city's amazing expressways, gawp at women in Tajrish, ride the train out to Karaj for 20c, see the underside of Iran which has nothing to do with Ayatollahs or Islam. Tehran is a brash, ugly and characterless city, but I've managed to entertain myself for maybe 3 months here, just hanging around.
OK, I hope that helps. Get yourself the LP guidebook (it's pretty good, most of what I've mentioned is in there), and, if you can, learn the Persian (Arabic) alphabet. I say this because for about 6 bucks you can buy a fantastically accurate and useful 1:1,000,000 scale road atlas of all Iran's many roads, marking sights and petrol stations which is in Farsi and far better than the English language production (or it was when I was there). It's by gitashenasi and can be bought at bookshops all over.
Good luck, try to use your two months to get off the well known tourist trail as it gets more interesting and original by orders of magnitude once you break off the Tabriz - Tehran - Esfahan - Kerman Gringo trail.
All the best
Daniel (in freezing Mongolia, now itching to go back to Iran)