Is there a reason why you have chosen to split your time between the Strip and Fremont Street?
I personally wouldn't stay on Fremont Street. If I did, it would be the Golden Nugget hands down but that is just a Downtown Vegas hotel trying to match the Strip properties (and doing an alright job). When we go to Vegas we always head down to Fremont for an afternoon or evening, but I'm of the belief that you've got everything you need on the Strip, why bother? Yes it's good to see "old" Las Vegas and there are often good deals to be had ($10 slot play at the Nugget being one of them) but I never feel totally comfortable in the area, and waiting for the Deuce back to the Strip is shall we say "interesting" in the evening.
If you want to split your time between properties I would look for a different hotel on the Strip. Although I would probably not go as far as recommending the likes of the Sahara or Stratopshere, you probably aren't going to get better quality rooms in Downtown Las Vegas. The benefit of the Sahara would be the monorail station (whisking you anywhere on the Strip) and not a bad walk from the likes of the Wynn. I've not stayed there but I am always impressed by the friendliness and cleanliness of the public areas, plus the hotel can often be very cheap. If you can bump your daily rate up a bit, you can even start looking at the likes of the Excalibur, Luxor etc.
Harrah's @ $39 seems a good price btw.
Sorry if I have gone slightly
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with regards to the Fremont Street part of your question. Best of luck.