Hamburg to Luneberg by train

These trains get so complicated. I am learning right now that trying to take the cheapest options always makes train/bus traveling hard to calculate. The problem is the stupid ICE trains are now so much more expensive. Long rides seem to always be 70-100 euros each way.

"...the stupid ICE trains..." Those are the exactly the trains I take, or try to. You could plan ahead , get the adv. discount tickets for as low 19 or 29 Euro per person. But then be advised that you locked yourself in time and date wise, and sacrificed any flexibility.

@ Denny.... I'm in the middle of the two ages you listed, the ticket price per person one way is about 12-14 Euro, have done that several times, ie, buying it from the DB machine.

BTW: You'll like Lüneburg, a picturesque, historical (undamaged in the war), relaxing small town, one of my favourite towns in Germany. Most likely, you just might be the only Americans around. From the train station walk down to the left, the first corner turn right, go straight , cross the bridge, on the right is Hotel Altenbruckertor with the Chinese restaurant attached, continue straight until you see the huge church , the Johanniskirche. The center (Zentrum or Innenstadt) starts there on Am Sande.

Wait a minute, that's just a local ticket. Should be a day pass that covers that. At the very least, a Niedersachsen Laender ticket for 2 is 26 euro.
Edit- Yes, Hamburg Verkehrsverbund all-zone group ticket is identical price of 26 euro.

1. learn to use the German Rail schedule and fare webpage (http://reiseauskunft.bahn.de/bin/query2.exe/en).

2. learn to spell "Lüneburg". Lueneburg will work, but the German words burg and berg are not interchangeable (although the Bahn website will sometimes give you a break).

"Are there any special passes"

Lüneburg is located in the German Land (state) of Niedersachsen. A Niedersachsen-Ticket, 27€ for two people, is valid in the state of Niedersachsen and also in the city state of Hamburg. It's valid for unlimited travel all day long (after 9 am workdays) on regional trains in Niedersachsen and all public transport of the the HVV, except those parts of the outer rings that are in the state of Schleswig-Holstein.

Edit: Sam, you're right. Lüneburg is inside zone E of the HVV, so a Gesamtbereich 9-Uhr-Gruppenkarte would cover their travel after 9 am workday (all day on weekends) in the entire HVV, including the part in Schleswig-Holstein, for 26€ (1€ less than the Niedersachsen-Ticket).

I got the Niedersachsen price from the DB site, but I guess they have not updated the new price. I learned that last year when I got a N-W day ticket out of the machine and it was a euro more than what DB showed.
And since he is going on Saturday, he can start before 9 am.

Thank you, everyone, for the responses on train and town. This is exactly the information I needed. I can't believe I misspelled the town. I thought it was the umlaut that was messing me up. I learned about Luneburg on this site and it sounds exactly like the kind of place we'd like. Thanks again.

" I thought it was the umlaut that was messing me up."

It was. 'u' is not the same vowel as 'ü'. You might as well spell it Lineburg. However, you can spell it Lueneburg, and that is acceptable and has historical significance. It's better than Luneburg.