Hiking in Tatra Mountains

My husband and I would like to hike in the Tatra mountains. Day hikes and stay in Zakopone. We plan to travel mid-sept. to mid-Oct. 2023.
Can we access the trailheads without a car, or is it a distance to get into the mountains.
Is there a cable car to reach higher elevations as a starting point for hikes.
Any other recommended lodging local besides Zakopane for hiking in the Tatras.

Thanks in advance for your help.