iPhone 4S to cheapo tv for picture viewing

Wife does educational beekeeping. She wants to use the pictures off her iPhone 4 and show them on a tv. She purchased a small HD LED TV and we connected it with a HDMI cable. Pictures are horrible.
What would be her best option. She doesn't want another laptop, she needs to be able to carry it with her to events, that's why we chose the small flatscreen.

You should be able to do this via Apple TV.

https://www.apple.com/uk/airplay/

Does the TV you purchased have inputs for composite video (red, white, yellow looks like connections for a stereo)? If so, this cable is worth a try. I've used it and the picture isn't bad. Cheaper than an Apple TV (though not by much).

I read the instructions that came with the tv (imagine that) they show either a phone or computer being hooked up using the VGA port. Going to try that.