There are three Ikea stores close to Frankfurt:
- East: Hanau
- West: Wiesbaden (Wallau)
- North: Nieder-Eschbach (Bonames)

To go to Nieder-Eschbach Ikea using public transport, you can take the U-Bahn line U2 from Frankfurt south train station, direction Gonzenheim. Change at Kalbach and get bus 29 towards Hohe Brück. Bus stop: commercial centre (Gewerbegebiet) Nieder-Eschbach (information and time-table on the website).

To go to Wallau Ikea, apparently you can take a bus from Frankfurt (or train to Hofheim, then bus) but I don't have more info (on their website they only indicate access with a car).

And of course you can also buy online and get delivery.