Surprised no-one's mentioned the Fender Mustang Micro (I'll never understand why they chose that name when there's already a 4/6-string using it), a matchbox sized modelling amp with a headphone jack that plugs directly into your instrument. USB rechargeable, the sound quality is great and you can stream to it via bluetooth which lets you play along with, for instance, a Spotify playlist. The latest model (the Plus) features 25 amps and 25 effects that can be chained together in whatever configuration you like via an app and stored in one of 100 presets, along with a tuner and a tap tempo metronome - the original is a little more basic with only 12 amps and 12 effects, and only lets you select one of each. Sound quality on both models is superb, really clear signal from your guitar and the modelled amps and effects are (mostly) great.
Absolutely love mine, the upgrades on the Plus are fantastic but the original is still a great little headphone amp. Both can double as an audio interface for use with DAWs as well, although I've not tried that so can't comment on how good they are.