Helicopter pilot reported a NMAC during pattern entry with a departing aircraft. Helicopter pilot hovered until clear of traffic and then landed.

Narrative

I was flying a helicopter from the ZZZ to ZZZ1. Accompanying me was my XX year old daughter. We had gotten up early in the morning and flew approximately 8 hours; stopping 3 times for fuel; over an 11 hour period. About 20 miles out of ZZZ1 I noticed a TFR ring on my Multi-function Flight Display (MFD) (assuming the info came from ADS-B.) Confused as to why a TFR would be this far out; I called ZZZ2 Tower who verified no active TFR's and gave contact info for Approach. I was unfamiliar with the area and was concerned I may have been flying into something that had not shown up on my prebrief that morning. I contacted Approach and got VFR flight following just to be safe. They handed me off to ZZZ1 Tower. I informed tower that I was unfamiliar with the airport; but that I was instructed to park the aircraft on Taxiway 1. I said that my hands were full and that I didn't want to go heads down to pull up the airport diagram for a direct landing. ZZZ1 said no problem; 'we'll bring you on Runway XX' and give us taxi instructions from there. Tower instructed us to enter a right downwind for XX. Upon entering I could not recall if they asked me to report or not. I didn't report. At that point I spotted taxiway 1 and pondered asking for a direct landing; but opted to continue to fly the pattern. I flew a right base and at that point we received an altitude alert (typical with our avionics system) and a traffic alert. My daughter questioned it; but I assumed it was a plane on the ground and told her it was okay. I turned final; and on short final I observed an airplane departing on XX. I do not know where the airplane came from. I came to a hover at the end of XX and waited for instructions from Tower. When none came I told them I was at the 'end of XX' and they proceeded to give me taxi instructions to taxiway 1. At that time I did not recall whether I was cleared to land or not. I did not recall any other traffic in the pattern or being given a takeoff clearance. However; I do recall being tired; that my kid was hungry; and that I just wanted to get on the ground.