Going from IR to RF...Which remote will do it all and not break the bank.

At that price you will probably be stuck with Logitech or Harmony. Not a great option in my opinion. If you are willing to spend a little more ($450-$500) you can get a Pro Control remote. It is made by RTI which is a great brand. I have had good luck with them in this price range, and the software is very intuitive and easy to use.
You may also look for something on eBay from RTI as the older RF remotes go for very reasonable prices on there. Maybe a T2C etc...
www.procontrol.com
www.rticorp.com

Since you have a TV outside, you'll need some local IR, too, so I'd suggest just adding a cheap universal remote to "keep outside", and add the Next Generation Remote Control Extender, for RF control of the Denon and FIOS box.

http://www.amazon.com/Next-Generation-Remote-Control-Extender/dp/B000C1Z0HA/ref=sr_1_1?s=electronics&ie=UTF8&qid=1359242020&sr=1-1&keywords=next+generation+remote+control+extender

A URC WR7 and the Next Gen extender would be about $60...

Jeff

If you have a smartphone could go with iRule and an IP to IR device. You didn't post your AVR's model number, but it could have a remote app for IP control.

You missed my point. Buy another, cheap universal remote like the one I linked to. You'll keep it "outside" (or nearby indoors) for use outside. You'll want that remote to be programmed to use the outdoor TV (power on/off, volume, mute, etc.), and have RF capability to control the set-top box inside. Hence the NextGen piece.

If you just carry your "indoor" remote outside, you won't have the IR codes correct for the outdoor TV unless they happen to be the same brand (and also use the same IR set).

Interference is unlikely due to the very low chance any of your neighbors have a Next Gen and due to the very low power involved. Logitech RF requires an expensive logitech RF remote, of which there are only 2 current models. Next Gen works with almost any remote that uses AA or AAA batteries.

Logitech also makes a relatively expensive IR repeater that works with any remote.

Not sure what you mean by the audiovox. They make leapfrog, where you aim your IR remote, then it goes via RF to an IR transmitter elsewhere. This is how a typical IR extender works. Most work fine but require aiming and both a transmitter and receiver. They are cheap and universal. Audiovox also makes a purely RF extender which only works with Acoustic Research, Nevo and One-for-all RF remotes, all of which are discontinued and expensive. I happen to have a couple of these remotes and really like them. So I do recommend one, if you can still find one.

Unlikely.

It's much better than the IR-to-RF repeaters like the Audiovox, X10 Pyramids, etc. as there's no IR receiver to pick up interference from sunlight, LCD screens, CFLs, etc. A built-in RF remote will probably work better, but will be much more expensive.

Jeff

More often its the RF receiver that picks up RF interference, and puts out IR junk signals that bombard IR windows of components. Blocking or making it useless.

How do you choose which MHz extender to buy. I have fios QIP7100 P2 box.

Either will work since the RF frequency (418MHz or 433MHz) of the NextGen remote extender has no direct communication with the IR devices being controlled. The IR signal originating from your remote will be converted to RF (which doesn't require line of sight) and is sent to the RF receiver pod where it is converted back to IR allowing the receiving device (such as your Fios box) to accept and carry out the command that was sent from the remote. NextGen's latest remote extender, the Genius, is available in five different frequencies allowing independent control of up to 5 like devices.