You can also arrive here with Ethiopian Airlines from Addis. There are 2-3 daily flights, that cost about 130-140 USD the return ticket. You fly to Dire Dawa, the main city 30 kms away, and from there you have to take a minibus to Harar
There are direct buses Addis-Harar that take 10-12 hours and cost 56 Birr (5,6 USD). The buses leave Addis central station at 6am, though they actually leave at 6:30, BUT you have to be there at 5:30am and wait, as the seats are not numbered and, even buying the ticket in advance, you might find the bus full if you arrive late.
At the end of the afternoon, you arrive to Harar bus station, that is just outside the walls. Buy the return ticket in the station as you arrive, just in case.
These old 50s PEUGEOT taxis were everywhere in Harar, though I didn't find them anywhere else in Ethiopia. Somehow reminded me to those old cars you can find in Havana (Cuba) that must be repaired by their own drivers with invented pieces. I never really used them, as distances are really short in the old town and I had nothing to see in the modern town.