assuming this is for my kingdom au!
-- first meeting.
they meet after hal starts his patrol in gotham kingdom and he hears a noise above his tavern room! he leaves his room to go onto the rooftops to investigate the noise and he sees the dark knight gravely injuring a talon. he assumes that the dark knight is the villain in the scenario due to the screaming coming from the talon and attacks him but the dark knight gets away
with that, hal decides to do some reconnaissance in town to listen about rumors / sightings of the dark knight to try and stop him but he eventually finds out that the talons are the bad guys and theyre forced to make an alliance despite their rocking meeting to fight against a horde of talons together :]
-- favorite keepsake.
for hal - i think later on in their relationship, bruce commissions a weaver to make a cloak / shawl just for hal with a symbol that only the two of them would recognize the embroidery under the collar of piece (he asked alfred to embroider that symbol, jsut to keep it a secret)
for bruce - mayyybe in a situation where hal is exploring the catacombs of arkham castle and discovers a secret compound that not even bruce could find (due to magic properties), he finds an old commissioned portrait of bruce's parents when they were still alive and gifts it to bruce
my brain is a little empty rn (sorry) and i havent gotten so deep into my plot yet, but i think probably the main secrets they would hide especially early on would be injuries or missions. i think eventually they would both get really mad at each other about hiding injuries or going on patrol on their own since they always find the other gravelly injured and having to nurse them back to full health. they only find out because their separate investigations overlap bc they come to find the same conclusion just in different ways :)
training together! maybe eventually bruce invites hal into the kingdom as a combat advisor / magical advisor due to the appearance of more magical related incidents in the castle city and its also an excuse for them to be together a lot :)
i think it might be fun for them to do like faux hunting / horseback riding across the lands outside of the kingdom walls too, just so they can breath and forget about all their responsibilities even for just a minute
(note: now realizing that u might have not been asking about my kingdom au)