Finding rooms with a balcony is a bitch, especially if you aren't willing to pay several hundred a night.
Cheapest option is IP. All of their rooms have balconies. Strip view also allows you to partake of the loud music from Carnaval Court. Personally I'm not bothered by that, but you may be.
MGM has the terrace suites which have giant balconies, most with a hot tub on them. These are quite spendy and must be booked well in advance. They all have some Strip view: south side-NYNY, Excal, Luxor, Mandalay and Trop. north side: everything else.
NYNY has at least one suite with a balcony, but it appears to be made of unobtainium for us normal folk.
Here's an unexpected option on the higer dollar suite side: Rivera.
Allegedly, Sahara has at least one suite with a balcony.
The Villas at Wynn have balconies, but are astronomically expensive and hard to book.
The Cosmo is going to be your best option. Its cheaper than everything else I've mentioned so far except the IP.
Oh, I almost forgot the garden rooms at the Trop (if they're still around-I'm out of the loop) and they were quite cheap. I wouldn't put them in the view category exactly, but you can see MGM. NYNY
Signature & Platinum are good options as well, but aren't actually on the stip IMO.