Any suggestions of a place to stay that would be on the beach with free parking that you would give 4-5 stars? I have read that North Myrtle Beach is the best place to stay.
4-5 stars is limited in the MB area. DH loves MB, so we've gone there an average of 1-2 times a year for the past decade. So far I've never stayed anywhere I considered even a 4 star, but that doesn't mean I can't recommend decent places to stay, just not 4-5 stars IMHO.
Myrtle Beach can be a little sketchy. I also recommend the North Myrtle Beach area. For families with children, I always recommend Dunes Village Resort. It is clean and has indoor waterslides, hot tubs and 2 outdoor pools and a lazy river.
Some friends recently stayed at Marriott Grande Dunes and said it was lovely.
We love Dunes Village. It's our "go to" resort when we can afford it. In October, prices should be reasonable. Marriott was never in our budget, but it looks like it would be nice and probably meet your star criteria.
Avista was HORRIBLE for us, there were several loud teens well in to the wee morning hours that kept us awake!
October is a great time for that area bc rates are typically lower

This is a great website to see decent reputable hotels in both Myrtle and North Myrtle:
http://www.visitmyrtlebeach.com/STAY/
Here are a couple suggestions..
The Camelot
Hotel Blue is fairly new
Coral Beach
Island Vista Resort (a little pricey at times)
Sandy Beach Resort (also fairly new)
Hope some of these are helpful
Have not stayed in Avista - keep hearing good and bad about it.
Island Vista looks like it would be nice, I have priced it out several times, but value for money-wise it never worked for us.
We did stay at the Sandy Beach Resort. The nice part about it was it is near the new boardwalk and you can walk to the Family Kingdom. Not sure if FK is open in October? We were there in summer, so it was fun. But there are not as many water activities within the resort. Also we learned that one section has safes (I believe the older rooms) but the newer ones (condos) do not because "the owners saw no need for them." At least that was the case when we went (2011?)
We like the Marriott Grande Dunes on the beach:
http://www.marriott.com/hotels/travel/myrgd-myrtle-beach-marriott-resort-and-spa-at-grande-dunes/
We also like the Marina Inn at Grande Dunes, but it is not on the beach. It is lovely, though, and they have beach access either with a shuttle or with self-parking:
http://www.marinainnatgrandedunes.com/
Both properties are
AAA four diamond resorts. I'm not sure what your budget is, but October is off-season and rates are lower.
Sounds good if within OP's budget.
Yes, the original post mentions "budget trip" and then everyone recommends the high dollar $1200-1500 places to stay. There are a ton of very nice places to stay that you can get 2 room ocean front with bedroom, kitchen, and living room overlooking the beach for $600-700 a week.
Dayton House, we loved it.
I would rank my favorites of where I have stayed:
Dunes Village (best)
Caribbean Resort (we like these this and DV because of the water slides and other pool/lazy river stuff and decent, for MB, service)
Dayton House (pleasant, and the zero entry pool was nice with a toddler)
Sandy Beach (no real complaints)
Also, we have visited, but not stayed at the Ocean Reef. I got to peek into their "Parlor" corner rooms. I would LOVE to stay in one of those someday, without small children (when we visited, the balcony rails seemed widely spaced at Ocean Reef, and we had a toddler.) Look at the room layout online and you will see what makes the rooms appealing.
Caribbean Resort is nice, but I recommend not staying in Jamaican building. It was smelly whenever we walked near it, and seemed kind of scary at night. So unless they have done some extreme renovations there, I'd opt for a different building. Also be aware the Chelsea condos are across the street. The other 2 buildings at this resort are fine (Dominican and Cayman.)
Have fun at the beach! October is a nice time to go. We just can't anymore, due to school schedules.
Almost forgot, my parents stayed at Towers on the Grove in NMB, and enjoyed it, but again, I don't think there were as many pools, etc. They felt it was rather isolated, but it was brand new and upscale.