HIFIman re400i, inexpensive, very neutral. if you are like good quality and not overpowering bass. pair it with sony hybrid tips or any cheap copy of them. does work well with mobile phones but scales very well with an amp.
some other options, (the ones i own atleast.)
fiio x1 2nd gen ( very good bass and treble but the fit and weight of them can be a problem for some people )
audio technica e40 ( fit can be a problem and emphasis on bass )
audio technica im70 (excellent if you can find them, sound better with amps )
meze 11 neo ( boring sound )
vsonic GR07 BE ( where's the bass at ? )
KZ ZS5 ( excellent value for money, the sound stage and imaging is unreal. they are huge )
overall i believe HIFIman re400i will be a good option worth considering for you because you will be using them on the go and will not be using any amps, they are very lightweight and easy to power. due to their small size they isolate better.