During my stay in Vegas, I will be staying in a hotel(New Frontier) on the strip.

I would be having a rental car.
But I heard it might not be easy to park.

I wanted to know how we could safely travel from our hotel to Downtown and back, for Freemont experience , in the evening. Please also let us know how much time it would take.

Since no one has answered yet I'll top this for you. I haven't driven in Vegas on any of my 20 or so visits but I can tell you that it would be less congested to take I-15 to downtown. I'm sorry I can't advise on parking, maybe someone else out there can. Good luck.

New Frontier is towards the end of the strip, so driving might not be too bad into downtown. The valet at your hotel should be able to give you directions. Even in a cab it shouldn't take you more than 15-20 minutes to get there.

As for parking, I assume you mean at your hotel? I think most of the hotels have parking for their guests. All the hotels we've stayed had free valet parking, a tip to the valet of course.

There is valet parking at every hotel/casino. And they built a fairly large parking structure downtown in recent years, just for Fremont Street.

But I never drive in Vegas. I know at some point I will be partying, and I never drink and drive. The scary part about Vegas is if you look around and see all of the other people partying and then notice how heavy the traffic is, you realize that there must be a lot of people partaking and then driving. In 20 years of visiting Vegas, if I was unable to catch a flight, I have always parked my car when I arrive and there it stays until it is time to drive home.

My suggestion would be to take a cab to somewhere like the Golden Nugget and get a cab back.

Alternatively you can take the bus, but on your return you should go to the downtown bus terminal as the queues for the buses back up the strip build up rapidly 1 or 2 stops out of the terminal. By the third stop the bus was full and not picking extra passengers up. One slight disadvantage is that the bus terminal when I was there was a bit on seedy side, I also ended up walking up a very very quiet road, which was a bit unnervy (typical scaredy cat tourist that I am).

As a compromise the bus there (it stops at one end of Fremont st (or close to it) and the taxi back may be the best option.

Wouldn't bother with the car. By the time you have valet parked it, it would have been easier and cheaper to use the cab

Oops forgot, 20 minutes either way, depending on traffic sounds about right.

Don't miss the Freemont experience it's excellent! If you fancy a gamble you'll also find the casinos have lower table limits, and supposedly the slots are looser (hype?) than on the strip. The food options at The Golden Nugget which is adjacent to Fremont street are well worth checking out.