In general, the advice I've always heard from everywhere is that whether in an exit-interview an informal conversation, or even in an a situation like yours where advice isn't being solicited, the best course of action is to say as little as possible. Basically say nothing of note, and avoid specifics. Especially when the case is that you're leaving for a better (or more suitable/compatible) offer elsewhere, the best thing to do is just say that. It's honest, vague and not going be taken as offensive or negative.
The reason for this advice to generally say nothing is because you're in a situation where you have nothing to gain, but could potentially burn your bridges or hurt your reputation if you say something negative, or something you say is perceived negatively, or someone takes offense at it. In the best case, you gain exactly nothing, and in the worst case, you hurt yourself... so from a cost/benefit or risk/reward perspective, the math on this type of situation is incredibly easy, and overwhelmingly in favor of saying nothing.
If you're really interested in leaving feedback or suggestions for whatever reason (Which again, is not recommended), the best way to do it is anonymously. Write up what you want to say now, stash it somewhere safe, and come back to it in a few months. If you still want to send it off, you can (of course, keeping in mind that you don't want to say things that would personally identify you, or come off like you're bashing the place or any person in particular). But again, since you have nothing to gain from sending off your anonymous correspondence, I would advise against it. Writing it out anyway can be a helpful exercise in introspection and may even be cathartic, so just gathering your thoughts is not a bad idea. Sitting on it for a while gives you time to make sure you're not acting out of emotion, the passage of time helps anonymize you, and you also get more time to consider whether it's really a good idea to offer feedback to your former employer. (I've gone both ways, myself, but choose not to offer significant feedback the vast majority of the time, for what that's worth.)