... any advice whether I should then spend 1.5 days in Tel Aviv or go to Jerusalem?
I will have another 1.5 days at the end of the trip on a Friday / saturday (am at a conference in between).
Main worry is to get a cheap transfer back to Tel Aviv from Jerusalem on a saturday... Any experiences?
And for a culturally interested person what are the highlights of Tel Aviv?
I suggest going to Jerusalem. Take the Nesher "sherut" (shared taxi) service to your destination. These are 10-set minibuses that cost 58 NIS and leave when they fill up (if you are the last one let off you will get a nice tour of the city).
When you leave, if you go to the airport from Jerusalem you can book the Nesher sherut to take you back to the airport (call them at least one day in advance).
Note that the airport is located between Tel-Aviv and Jerusalem - driving time is 20 min from T-A and 40 min from J'm.
To go to Tel-Aviv from the airport (or back to the airport) you have to take a regular taxi or the train; there is no sherut service.
Note that the taxis and sheruts run 24/7 ; buses and trains do not run on Saturdays.
Culture in Tel-Aviv - museums, theatre, music, galleries, etc. Look at "Time Out" Tel-Aviv magazine for ideas:
http://digital.timeout.co.il/english/
Where is the conference?
Tel Aviv, Jerusalem and the Airport are all well connected.
From the Airport, you can either take the Nesher service taxi to Jerusalem (it will drop you off anywhere you want)
Of you can take the train to Tel Aviv - about an 11 minute ride depending at what station you get off.
To get between Tel Aviv and Jerusalem you take a bus, or a service taxi.
Buses operate between the central stations of both cities, Saturday Evening through Friday afternoon.
The service taxis operate 7 days a week and go between the Tel Aviv central bus station, and the service taxi terminal near Yafo Street #44 - where the Khalifa Shoe Store is...
Correction to the last sentence of #2. The service taxis (sheruts) leave from 44 Jaffa Road (corner of Harav Kook Street), a better description that you'll be able to find on a map - which doesn't mark shoe stores! - but only on Shabbat (Friday evening and Saturday).
On weekdays they leave from outside the central bus station.