That all depends on who you ask. For a lot of us, we never had a supposed 'purpose' to begin with. We were just stuck with what we had. As a kid finding motivation wasn't hard as everything was new to me but something I found that brought me motivation and happiness was art. For you though that may be different, you've been around for long time so it may be harder to find motivation but it's not impossible. I'm sure you there is still plenty to discover on Earth. Maybe you could find motivation in that. If doing good is the thing you need motivation to keep doing then look at humans. Humans have tons of reasons to do good. One reason may be because it makes others happy and in turn, makes them happy and another reason may be because they feel the need to make up for the terrible things they've done in the past.
Here's the thing though, Aziraphale, you don't have to go out of your way to do good anymore if you don't want. You don't have to do anything anymore if you don't want. If doing good doesn't motivate or fulfill you then you don't have to do it. Find the thing(s) that make you happy and do them, without guilt and without fear of consequence. You don't need a purpose to be motivated and having a purpose dosen't necessarily mean you'll be motivated. You don't even have to stay on Earth. You and Crowley can leave Earth and never return if you so please. The choices and the possibilities you have are endless! All you have to do is find the ones that fit you. But you also don't have to rush. You literally have all the time in the world.
And if you want, try asking Anathema. She's probably in a similar position as you as she's also had a purpose her entire life as the great great granddaughter of Agnus Nutter and is probably also trying to cope with not having a purpose anymore. Maybe you could help each other. Another similarity between the two of you is that you aren't alone. You both have someone who can help you through this. You have Crowley, who's probably trying to figure this all out himself as well and she has Newt, a man who has never had a single thing figured out in his entire life. You also have us and I'm sure any of us would support you when, or even if you find the conclusion you're looking for, assuming any of us will still be alive when you come to your conclusion.
I do hope it helps.
Crowley: Well that was thorough.
Aziraphale: I appreciate the time you have taken to write this out for me, dear friend. I believe I shall be rereading your words a few times in the future when I feel a little lost as well. I suppose this whole 'free will' thing is just a little new to me and that's what is strange. I think I do still want to do good in the world though. Though perhaps I won't feel so guilty now when I want to bake and read as well.
Crowley: Want me to get Anathema for you then?
Aziraphale: Not just yet I don't think. But perhaps we could have a spot of tea together once I've worked my way through this a little more.