Best running apps for my iphone and best heart monitor

I downloaded Strava for my cycling but since i started running i bought a Polar H7 BLE HRM that pairs up on both my iOS and Android devices. Works like a charm

I am at a point where I need to more accurately account for calories burned. I have an iphone. What running app do you all recommend for accurate reading

As far as route and pace tracking is concerned your main options are:

Endomondo - Personally my recommendation as it has some good analysis tools on the website and app
Runkeeper - Also good and whilst I recommend Endomondo I also use Runkeeper in parallel
Strava - Powerful, biased towards cycling and running but very popular amongst serious trainers. The premium version is quite expensive.
Runtastic - I'm less enthusiastic about this as the free version is very limited and the charging structure for paid features is quite involved. I also found it hammered my battery life
MapMyFitness - I would not recommend at all, personally I've found it unreliable, inconsistent and the web site is very user unfriendly. that said lots of new trainers rave about it.

Try all of them and see what you prefer, but the main thing is to pick one and stick with it.

As far as HRM is concerned, I share your view that a wrist mount is more useful on the fly, I use a Polar FT60, but again all you're going to get is what I have from most people. Polar is a well established brand.

If you want to splash out, and running is your main sport, then a Garmin watch with HRM does both.

I have a Polar RS300X heart rate unit, great device, but in order to enable the testing of various mobile apps I purchased n Polar H7 BLE HRM strap and now simultaneously use the RS300X watch, as well as 3 apps on my iPhone, Polar Beat, Digifit, and Endomondo. I have been running various tests, both indoor and outdoor and am about to draw my own conclusions, which I might just blog.
My opinion:
* The watch is great as it is wrist mounted and can be used to check and set laps, or other functions on the fly, the post exercise data is far less limited. One can use it without fear of battery drain, but there is no GPS built in, this would need to be added via the optional Polar GPS unit.
* Polar Beat comes in as my favourite app. The interface is excellent, it syncs seamlessly to my polarpersonaltrainer profile, as well as to the new Polar Flow. Post exercise data is excellent, features such as voice prompts, tying up with music playlists are all great. Downside, using this method outdoors for extended periods drains the phone battery fairly rapidly as both bluetooth and GPS are running. Full functionality requires in app purchasing, but no monthly premium is required.
* Digifit comes in as my next favourite app. To sync with the H7 one has to first purchase the sensor upgrade, not expensive. The interface is excellent, slightly more detailed than the Polar Beat. it syncs seamlessly to my Digifit profile. Post exercise data is excellent, features such as voice prompts, tying up with music playlists are all great. Downside, using this method outdoors for extended periods drains the phone battery fairly rapidly as both bluetooth and GPS are running. The upgrade pack is great and caters for 90% of what I want out of the app, but full access would require a premium monthly subscription.
* The app I would drop first is endomondo, I have nothing against the app, it works well with the H7 which adds the hrm training to it's functions, but the post exercise data is really lacking compared to the other two. Any type of decent reports or tests would require a monthly premium subscription. Again, bluetooth and gps battery drain is relevant.

I will eventually settle down to using just the Polar watch for ease of use and visibility. coupled with the Polar Beat app for the great feedback it gives me.

To be noted, my training consists of mainy indoor cardio and weights, and outdoor dirtbike motorcycle training, so cycling is not a requirement for me.
Although all apps have cycling listed, this would be GPS and HRM based, giving distance, speed, averages, etc. For cadence they would require the additional compatible cadence sensors, as would the current watch I have.
There are obviously many many more apps or solutions around, as mentioned.
Hope this info helps..

I am an admitted fitness app junkie. I've experimented with almost every app out there and I've never been happier than with my current setup. It requires a iPhone (4s or 5) and a BLE (blootooth) HRM. I think it also works with droids.

I use the Wahoo fitness app to track workouts. I track HRM & GPS, however, its also capable of tracking (cadence, pace, etc.). Once the workout is tracked, it can be synched with several other fitness programs (MFP, Garmin Connect, Stravia, MMF, Nike+, just to name a few).