Taking my Ph.D. advisor out for dinner after graduation

What is the professional/moral way of doing this?

I think that if you have never invited/been invited to a casual gathering involving the advisor's family, it will be awkward to do so now. If you feel like a one-on-one dinner invitation is too much, how about a lunch appointment?

I will say this - many universities have strict rules on receiving expensive gifts from students/subordinates. If your meaning of precious is simply "of significant emotional value" (say, you made a piece of art yourself, or found a book that they really like) that's fine; if you mean expensive (say, an expensive watch) - your advisor may not be able to accept the gift at all (or, as is the case in my university, will have to report the gift and then give it to the school).

Since you have completed your doctorate, you are no longer bound by gift rules, I suppose. Your relationship to your advisor now changes from one in which you have a subordinate role to one of collegiality.

I don't see any particular issue here, but suggest, pretty strongly, that you invite the prof and his spouse. You don't need to invite the whole family, as it can be a more adult affair with just you three, or you three and a "date". Unless the spouse is in the same field, the conversation will be more general and interesting, I think.

Presumably you aren't strapped for funds at this time or you wouldn't be considering this. If he understands that then he won't necessarily be uncomfortable accepting the invitation.

It is good to thank your advisor. But things of monetary value aren't really that important. Saying thank you is more "precious", actually.

But it is also especially good to maintain that collegial relationship and let it develop over time if you can. But if you are staying in the same general area or expect to return, doing this in a year or so, rather than immediately would be even better, IMO.

First, congratulations.

Second, thanks for wanting to thank your advisor.

I hope what's "precious" about your gift is "appropriate" and not "very expensive". If the latter, perhaps reconsider, or wait a year until you've been employed in industry so there's no question that you can afford it.

Ask him out to lunch - not dinner with his whole family. Extend the invitation in a way that allows him to say "no" graciously.

Finally: when I defended my dissertation my advisor and his spouse asked me out to dinner and gave me a small gift for my then one year old daughter. (I had moved away to a job so they couldn't include her or my wife.)