I doubt there's much of a direct use for the aeliopile itself. In order for it to be capable of real work, it would need to be pretty large. That's probably beyond the metalurgic abilities of that era.
It's best purpose is as and idea generator - a means to an end. A good many of those ends need additional technology development
1) right.
2) some of Hero's other steam toys (temple door openers etc) probably are a better place to start than the aeolipile
3) see the following
Rome gets steam power in 150 C.E. (Multi-page thread 1 2 3 4)
Tiberian
AH Challenge; Rome Discovers Steam
The Cobbler
Yesterday's Tommorow: A Plausible Roman Steam TL (Multi-page thread 1 2 3 4 5 6)
DonMegel
Hero's Handy Dandy Steam Slave! (Multi-page thread 1 2 3)
Geekhis Khan
WI: The Long Low Steam Age
tormsen
Plausibility check/WI: Aeolipile used as an engine?
ScorchedLight
Aeolipile: A Roman Steam Engine? (Multi-page thread 1 2)
Jape
Roman Industrial Revolution (Multi-page thread 1 2 3)
Saepe Fidelis
N00b WI : Roman steam-powered industrial revolution !!! (Multi-page thread 1 2)
Petike
Roman railroads? (Multi-page thread 1 2)
acgoldis
Heron's steam engine (Multi-page thread 1 2)
Hypa
Steam! But in Greece?
Marr965
Hero of Alexandria points Rome towards the Space Age (Multi-page thread 1 2 3)
Sinaz
Hero's steam engine triggers Greek industrial revolution? (Multi-page thread 1 2)
acgoldis
Industrial Revolution in Rome? (Multi-page thread 1 2)
Cornivus
Term Paper: From Aeolipile to Locomotive (Multi-page thread 1 2 3)
DominusNovus