you just want the biggest battery you can find in your budget really. i got an LG XPower for $60 to replace an LG Volt and it has a very large battery and easily lasts me all day even while goofing off with games.
but it may not have all the bells and whistles you want such as a super large screen. just do some looking around some sites and see what pops up in your budget. if you're budget is almost limitless you'll have more options obviously but if it is lower, then something like the XPower may be a decent option. i use it as a second phone along side a new iphone and it does not leave me wanting more. even compared to the newest iphone i use every day as well. i'm not a hardcore mobile gamer but then again i don't believe any of those games take high level resources either.
of course second best option is to get a large external bettery to keep with you. that will easily let you go easily a day without needing to recharge. at least 10,000 MaH. they pop up on newegg all the time in flash sales for under $20. i got a 15,000 one from sams club around christmas for $20. keeps my table streaming netflix for most of a day when i'm traveling. no more scrambling for a power plug in airports for me
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