Endomondo was what we started with.  I have since moved over to Strava and like it a lot better.  I use an app, TrackerBooster on my droid to help ensure gps lock stays.  Your best bet for accurate mapping of your ride, is a dedicated GPS, like a Garmin Edge series unit.  You can upload the data to Strava too, which makes it a bit more fun.

Personally I am a fan of endomondo, I think it provides more the same type info you will see on a garmin edge.  The ability to import and export gpx file is very nice as now you can do other things with the import from your gps device to endomondo if you choose.  I have used may my ride and strava, they all are similar and still have some features others don't provide. I know it sounds crazy but I use endomodo on my iPhone and then export the gpx from it and upload it to strava  because I like some of the reporting. In strava.  several friends use endomondo and it to has the sharing feature of strava.
 
As to the external battery question I use a mophie external battery charger/case that I like very well, I haven't  ridden long enough to max it out but would expect to get at least 8 hours out of it before drainng it and then you would still have the internal battery.

No RBENT group I know of on STRAVA so if you want to make one Mizta, go ahead and post the info/link here.  My Dave is on Strava, as is Jim, and Peggy too.  Lots of bent riders on Strava, mostly in the BF 50+ group or the Bacchetta Riders group.

I've been unable to find a computer less expensive than my iPhone that does what I need it to do.  Unfortunately, my iPhone doesn't have enough battery life to last my longer rides (MS150 and the like).  I do like Strava better than the other apps I've tried.

+1 for Cycle meter. This app is really nice, self contained, will connect with ANT enabled add on accessories like cadence sensors, heart rete transmitters,etc. It shares via .kml files and uses google maps to display info. You can import routes and compete against friends or against yourself.
 
It is pretty conservative with battery life as far as apps go but I do have a spare battery reservoir that I can plug in.  It did complete the Tour de Cure metric on one charge with power left over. I keep mine on the handle bar and it will announce average pace average mph, currend mph, ahead/behind best/avg/slowest pace, etc.  Announcements are customizable. I have a post on page 109 of did you ride today thread that has a link to its output.  Or, try here: https://maps.google.com/?q=http://share.abvio.com/55ef/ccc2/4c8c/272f/Cyclemeter -Cycle-20120728-0715.kml < edit > Correcting link < \edit >
 
The one thing it is currently missing is a good profile feature. The included one is a bit weak. However, there is an active design team behind the app and updates have been fairly regular and worthwhile.
 
All of this said, I will probably be getting a simple computer mounted if I start doing rando again. I'd have to carry too many spare battery packs for the iPhone for longer rides.

I am using the paid version. It is the best money I have spent on any app so far. It is easily worth three  or four times the $5 I paid for it. (it also tracks my runs with pace per mile, avg. pace, etc.)
 
 
Carl

iPhone rebooted on me again today, I'm about ready to take the plunge on the garmin 800.  Should you have any history, pro or con, please share them.