On foot:
The terminal is 1,5km away by walking, but it is a steep road, therefore, it can take around 20 minutes. It is worth it if you wish to enjoy the sights of Pera.
By public transport:
Take the funicular to Beyoglu, then walk 400 meters to the hotel. It is worth the experience.
By taxi:
The terminal is 2km from the hotel. A taxi ride usually takes about 10 minutes and costs around 6 euros.