I've just returned from Tanzania and after visiting all WHS there I want to share a few thoughts.
First of all, the country is completely open, no tests or quarantine required. For most countries it is e-visa or visa on arrival, so Tanzania is currently mecca for tourists from all the world. Masks are not used, only temperature is checked at the airports. In general, being there was like in time machine taking you back to the pre-COVID world - what a great feeling!
Visiting Tanzanian WHS is not very difficult, they are all accessible, even using public transport (to main cities). I did them in 11 full days (+ coming there and back) and this is a minimum time you should reserve. If you want to use public transport, add at least 3 days.
My itinerary was as follows:
Day 1 - Arrival to Arusha, plane to Dar es Salaam, arrival at night
Day 2-4 Pick up from hotel, safari in Selous Game Reserve and drive to Kilwa Masoko to visit Kilwa Kisiwani ruins (all in one package). Note that road from Dar to Selous is really bad, don't go without proper 4x4.
Day 5 - back to Dar, ferry to Zanzibar, visiting Stone Town
Day 6 - Stone Town + spice tour, plane to Arusha via Dar
Day 7-10 Safari in Tarangire, Serengeti and Ngorongoro
Day 11 - Kilimanjaro NP one day hike from Arusha
Day 12 - Kondoa Rock Art by rental car from Arusha and back
Day 13 - back home
Songo Mnara and Kilwa Kisiwani can be visited in one long day, but you should be in Kilwa Masoko in the morning. I think it can be visited from Dar es Salaam in two days, if you catch the earliest bus to Kilwa Masoko day 1 and the last one to Dar day 2. Road to Dar quite bad, takes around 5.5 hours.
Kondoa is a very large site with multiple locations. To cover most of them properly one day may not be enough. Doable in two days from Arusha/Dodoma. Road from Arusha is very good, ride to the first rock art site takes 4 hours one way.
Kilimanjaro NP is really not worth it unless you are going to the summit. One day hike until the first base is just tropical forest, but you have to pay 87$ entrance fee + compulsory guide (I paid 35$, but others wanted 50$). I went there from Arusha in rental car, but if you want to go on an organized tour, it may cost 300$-350$, including park fees.
All other national parks (Selous, Serengeti, Ngorongoro) have to be done in safari tour. In theory, you can do them on your own, but it is impractical and even more expensive, unless you are at least 4 people with experience in driving real 4x4. Be prepared for expenses - 4-day safari to Serengeti/Ngorongoro is about 750$ pp in shared car and basic accomodation (tents). Similar price for Selous from Dar or Zanzibar. The safaris are that expensive mostly because of government fees. Entrance to Serengeti/Ngorongoro is above 70$ pp per day and going down to Ngorongoro caldera is additional 300$ per car! But for those high fees you receive adequate quality - everything was on time and according to the schedule.
Self-driving is available and although rental car is expensive, using it for two days to go to Kilimanjaro NP and Kondoa saved me about 400$, comparing to the offers I received! Be prepared for frequent police checks and speed control in most unexpected places. I paid fine two times (there is a fixed fine of 13$ for all infractions), once being caught by a policeman sitting in a truck on the opposite side of the road. The second time was exactly while passing the speed limit sign.
English is widely spoken in places where tourists go. People can be very annoying towards tourists, but I met also really nice locals. Accomodation can be found very cheap. USD is widely accepted (EUR way less), but Tanzanian shilling (TZS) is the official currency and people usually prefer being paid in TZS.