We are addicted to Vegas and always stay downtown.
The public double decker bus, "Deuce" - can be taken downtown as the earlier poster pointed out.
Downtown don't miss things - well, there is one main strip down the middle that has the light show up above at night - it is free, just stand in the street and look up. The street is closed to traffic so there are venders out on the pavement (this is all the time). If you head south (towards the strip) a couple blocks you will see very old time stuff including displays of many of the early original neon signs - they are set up at the intersections and look great!
The casinos downtown have lots of slot fun - go to Mermaids and get free beads and those really tall drinks - very very boozy so be careful! They taste like freezees from your local corner market so its easy to go overboard! There are some fun cheesy souvenier places. If you go to the California, which attaches by an elevated walkway to the Main Street Station Casino, notice lots of people from Hawaii and parts of Asia! They also have a specialty Hawaiin ice cream shop in the walkway. Lappert's is the name. Several buffets downtown have a heavy Asian emphasis menu, too!
Golden nugget is the flagship and has an interesting pool and slide alongside a shark tank.
If you like to play blackjack, El Cortez has very good odds = they are south on Fremont about three blocks.
Downtown is more gritty than the strip but more friendly, in my opinion.