4-Days/4-Nights Ethiopia

you could fly to Lalibela for 2 days and on the way back as there are no direct flights to Lalibela, you could stop in Bahir dar for the day, do a half day tour of Lake Tana and a quick trip to the Blue nile falls the next morning.

IN fact, if you really want to pack it all in you could even take an early morning flight from Addis to Axum, where you have a two-three hour wait before your flight to Lalibela and you could get a cab and do a quick visit to the town to see the obeliscus and then to Lalibela, where you arrrive around lunch time, you could visit the frist cluster of churches in the afternoon, the second cluster the next morning and fly on to Bahir Dar in the afternoon, the next day you could acctually drive to Gondar do a quick visit there and then fly back to Addis on the forth day. I met some Ethiopians from the US this january who were doing a trip like this.While you wouldn't have the time to relax and interact with the locals much, you do get a feel for the amazing history and these really scenic places. You may wish to contact an agency to arrange for a guide in each of these places, to facilitate your visits.

The site that you referred to (Queen Sheba, Ark of the Covenant) is Aksum in the far north. Although it's not bad there, there are more interesting places, like Lalibela or Bahir Dar. With 4 days available, I guess you better stick to only one place, because domestic flights are frequently delayed or even cancelled, and then you have the risk to miss your onward flight from Addis.

I would suggest to take a return flight Addis - Bahir Dar. In BD you can visit Lake Tana with some old Ethiopian churches and the Blue Nile Falls.

Of course you can also stay the 4 days in Addis. You can always meet travellers in the Merkato area there, but with regard to sightseeing it's not so interesting.

You only have time for Lalibela and maybe a TESFA trip near there.
Lalibela will seriously blow your mind.
Go there.

If you only have 4 days, dont go to Axum only for seeing the arc of covenant, shebas bath and the steles, therefor alone I find it disappointing. I liked the whole place but not because of these sights (alone). Go to Lalibela and stay there on day 2 + 3, just to get an impression. The returnflight from Lali to AA stops in Gondar and Bahar Dar - so if you want to do a very quick glimpse... Dont pack too much in too short time, you need a bit do digest the impressions.

I am assuming you are more into history and with ur limited time you can fly to Axum and spend one day there and other 2 days in lalibela. Since there is a daily flight you will have enough time to enjoy both places.