Recommendations for traveler meeting locations in Budapest

Will there be cell phones available for coordinating late plane/ late train situations ??

Yes, we'll have cell phones.

Deak Ferenc ter is the most central point in the city. Three of the Metro lines converge there. Your daughter can get the 100E bus from the airport to Deak Fernc ter. There is a Starbucks there and I guess that is as good a place as any to kill time. When you arrive at Keleti station, take the M2 Metro to Deak Ferenc ter and go up to street level and locate the Starbucks. You can figure out what to do from there.

Until James E. chimes in, that is as good an idea as any, until a better one comes along.

A taxi to your hotel (or?). Is as easy as anything else. The airport taxi service is so simple and direct, you can't go wrong. Follow the black line on the floor to the kiosk outside. Tell the clerk where you are going, An attendant will put her in the right taxi and in 35min she will be there. They take credit cards. Cost about $20.

I guess if it were my daughter I would send her to the Lions Locker for breakfast.

https://www.lockerbudapest.com

I know the owners and I know they would take good care of her. Probably talk her ear off. If she wanted, they store luggage and its only a block from the Opera on Andrassy ut so if you are late she could do some sightseeing. Beautiful part of town.

Otherwise going sightseeing or someplace that requires a lot of walking raises the question of dragging luggage around. Crowded and less than ideally defined areas like Deak Ferenc ter might make it harder to find her; and the train station can be a bit of a mess unless you agree to meet at the center stairs that feed to the metro. Still, she is just standing with her luggage.

Starbucks!!!!! NOOOOOO!!!!!! Better a taxi to the NY Palace Coffee House. Actually, that would be a good idea too. Near the train station and a stunning introduction to town.

Greatly appreciate the quick and helpful recommendations!

Very cool that we can connect so easily this way.
The NY Palace looks like a terrific option where she'll (and we'll) get a really positive first impression of the city

thanks!

I'll second meeting up at The Opera on Andrassy because I flew to Budapest 1+ years ago to meet my husband who was finishing up a work trip and so already there. Taking a taxi from the airport was very easy, I am not a seasoned international traveler but had no concerns. Taxi pulled up right in front of the Opera and my husband was sitting out front under an umbrella table drinking a coffee - so perfect! We had the most wonderful week in Budapest, I hope you all have a wonderful trip!

Okay, so either way, the daughter just follows the black line and takes a taxi. Sure there are other ways, but why hassle when the taxi is so cheap.

The rest of the family has a couple of choices:
For the NY Palace I would take the metro.
Go to the front center of the train station and go down the stairs. At the bottom on the right there is an office where you can purchase TravelCards for the family. On the left are machines where you can also purchase the cards. Use the office, easier. Then follow the signs to the M2 (red) metro line. Then do this: https://goo.gl/maps/FiAHfScBcTx

For the Opera or my breakfast place I suggest a taxi. Call CityTaxi at +36 1 211 1111 and go out the nort doors of the train station and hop in the taxi. Again, there are other ways, but for about $7, why?