@ Zircon
In fact, with eight days, in my point of view, it will be better to stay in one country and not to try to "visit" three...
Michel

@ Zircon
In fact, with eight days, in my point of view, it will be better to stay in one country and not to try to "visit" three...
Michel
Do you have to start your trip in Baku and finish in Yerevan?
It's not the best combination for eight days, as you'll hardly have enough time to see the capitals. Tbilisi is the best of them all. If I could choose I'd skip Yerevan entirely in favour of Georgia. Yerevan was destroyed in a big earthquake and rebuilt in the worst of times (that is during the Soviet era).

Yes - already have a ticket landing in Baku and leaving from Armenia. Was to nervous to get a Visa for Azerbaijan after having been to Armenia. Read some reports that it was a no no. Cheap ticket methinks - 475 EUR from Copenhagen.
You can fly for half that price, return with Wizzair to Baku or Kutaisi, although you'd need two flights, eg. Stockholm-Budapest and Budapest-Baku. But they have no flights to/from Yerevan.

Wizz Air are good! But the dates I needed and from the town I could fly from - I found my ticket a bargain. Gone are the days when one had all the time and choice in the world.

I think your original plan is great, making for a very memorable trip. I did have another ten days in the Northern part of Azerbaijan this summer (staying in the mountains and in Russian kolchoz village Ivanovka) but spent only one week divided over Baku-Tbilisi-Yerevan as well. And took two night trains. I thought it was great to compare the three capitals, they've gone such different ways since their shared Soviet past.
Tbilisi is definitely the proper tourist destination of the three and perfectly photogenic. But that is actually why I was touched much more by Yerevan, I found it a more personal experience, That poor country really did get the worse deal out of the three countries.
On a Sunday morning I wandered the Northern neighbourhood around Envoy Hostel (nice, clean and friendly place and they do private ensuite rooms as well). I followed my ears and ended up at Zorovar church (1694). Armenian church services go on for hours with people walking in and out, all very relaxed. The continuous singing was hauntingly beautiful. Definitely recommended.
My favourite museum in Yerevan: the Sergei Paradjanov museum. No problem if you've never heard of the man, his life story and art work is very interesting in any case.
To sum up the three cities:
-I did not find one postcard in the whole of Baku
-Tbilisi sells beautiful postcards and expensive stamps everywhere you look
-in Yerevan I found just two places selling postcards and you can only buy stamps at the one enormous Soviet-era post office

To OP
I have a similiar plan, arriving in Baku on 14th May, leaving via Kutaisi, Georgia on 22nd May, 9 days. I'm still in the early stages of my planning but here's my itinerary:
14, 15th Baku, daytrip to Gobustan, night bus to Tbilisi
16th Tbilisi, night train/bus to Yerevan
17th Yerevan
18- 19th Based from Yerevan, doing a loop around Khor Virap, Tatev Monastery and Satan's bridge, Zorats Karer, Lake Sevan area
20th- 21st leave Yerevan to Georgia
22nd Kutaisi, late night flight to Lviv, Ukraine
I know most people will recommend I split the time between just 2 countries, but as for myself, I'm quite comfortable with this pace. I'm quite used to night bus/train travels and have no problem with it, as long as I get to spend 1 night afterwards staying at a hotel, etc.
Kelvin