I don't have a BOB. I do have some overnight stuff in my regular daypack in case I spend the night away from home, a fairly routine thing for me. It has toothbrush, toothpaste, a few meds, SAK, a change of socks and UW, sunglasses, etc. I don't know what I'd add to it in a bugout except maybe a few extra waterbottles (0.5 liter) and possibly some canned food. There's no knife except the SAK. So I think I'd be out within 1 or 2 minutes. I don't feel a need for a more serious knife and it would probably just cause trouble (urban environment). One item not mentioned is a radio. I have a tiny earpiece one that was $5 at Walgreens. It wouldn't occur to me to bring a cooking pot or firestarter or fishing gear or anything like that. The city is not going to suddenly turn into Gilligan's Island. I guess I'd bring my 440 mhz ham HT just because I have it, but wouldn't buy one for a BOB (some cheap FRS radios maybe).
I do have some supplies in my car (a couple dozen 0.5L waterbottles, FRS radios, a few other things) that I might try to snag even if the roads are unusable. I'd figure on total traffic hell and might try to exit by mountain bike rather than by car. A motor bike would be even better but in other regards is not really my style so I can't see buying one.
Computer: yeah, maybe I'd bring it (small laptop) or at least its hard drive. I do have off-site backups but they're way out of date. If I had my act together I'd update the backups more often (everyone should do that). I'll do that "soon" and may also post a thread with some ideas about how to do it.
Copies of documents (fireproof box?!): I'm having trouble figuring out what docs this could be. What docs would I need during a bugout? Drivers license, passport: originals are needed, not copies. Important business/legal papers: that should all be scanned into a computer and backed up remotely, or stored in a safe deposit box, not stuck in a bugout bag. Photos: digital rules, 'nuff said.