I took a route out of Rwanda into Tanzania and through to Malawi, in July this year.
I visited Lake Tanganyika (Kigoma) which was a great, if a little difficult, ride. I sense you're in a bit of a hurry, but if you have the time I'd recommend it very highly.
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After that I headed generally eastwards to Dodoma, another recommendation. It's the capital, but is all sand roads except the road with the parliament building and the main road around it. Quite strange. Nice place to stay.
On that stretch I took a wrong turn heading to Singida and ended up on 30 miles of deep talcum powder that took over half a day. That's to say, the whole route is good tarmac but you can find plenty of places to go off-road.
From Dodoma I continued the loop round to Mikumi, Mbeya then south into Malawi.
I think, by a close margin, Tanzania was about the friendliest country of the whole trip. But I was on my own, and in Tanzania you're not allowed to be on your own, so people will always look after you and keep you company.
There's a LOT of road building going on and I seemed to bump into Tanzanian road engineers all over the place, and they know exactly what roads are tarmac and which are still being upgraded. Just mix a lot with the locals and you'll find them!
Have a good trip.