I was looking for something like this once too.
One I've used and liked because first I can put the note names to be Do, Re, Mi, Fa... or A, B, C, D... and it's free if you used it on the website is this one: http://www.emusictheory.com/practice.html
They drill you with note after note and you need to say which it is. It also has the average time it takes you to identify each note. You can set a goal to lower it. No MIDI though.
They have a bunch of "drills" as they call them and are free as long as you use it them in the site.
Personally I wouldn't use something like this with the instrument necessarily, but I guess it depends on what you play just because being able to read the music and playing them on the instrument are different things. You can know the name of the note you are reading and even the fingering, but have bad intonation. You can also have great intonation and not be able to read music. They are separate skills.
Another (free) site that allows customization of exercises: http://www.musictheory.net/exercises/
I like this one because it allows you to work out acute kinks one by one (through customization) and then broaden your fluency.