Yes, you can easily spend a week in Budapest and fill your time - we spent four nights and could have used another and when we went, we were 33 and 30, not 50 and 75. Easy to enjoy a lot and do it at a leisurely pace that accommodates an active 75-year old.

Dohany Utca Synagogue, incl. the Weeping Willow
Szoborpark
KGB/Terror Museum
Andrassy Utca
St Iztvan's (Stephen's) Cathedral
Parliament and Imre Nagy Memorial
Heroes Square and Anonymous Statue
Danube Cruise

My adult daughters and I rented an apartment in Pest near Karolyi Park last July for a week. We had a lovely time. We visited a lot of the sites BigRuss mentioned as well as took several day trips - to Lake Balaton, along the Danube river, Herend factory, etc.

We used a driver (not a tour guide) for our day trips. Hungary is very reasonable compared to many other European cities.

You could schedule lunch at the Hotel Gellert and a "spa day" at their famous baths with spa services. The shopping is very interestng in Budapest, clothes, handcrafted objets d'art, etc. A day trip with a picnic to City Park and the zoo would be lovely as well.

There are lots of cuisine options in Budapest, not just Hungarian cooking. Very good French, Italian, etc. You can also take cooking classes or do a wine tour of the Tokay region.

If you are interested in any recommendations, let me know. If you do stay for a week, I would strongly recommend an apartment.

Thank you both - I think we are going to do the week! I like the idea of the day trips (and the spa day). LBloom - how did you find the driver? We are somewhat flexible in our specific dates, so are there any special events or things we should try to plan around?
Thank you for all the helpful insight!

For a fun time (did it with my daughter) go to the "Hungarian House of Wines" over by the Hilton hotel. You go in to a cellar and for a modest fee you receive a stamped logo wine glass and can go around and try over 150 wines on your own with a package of wine crackers to clear your palate. I believe that they sometimes have a guided tour guide but each wine has a plague with its history,geography and points-very interesting!
Also, take the public bus out to Statue Park where the old Cold War statues are now located-fascinating and easy to do. Its about a 15 minute bus ride.

I spent a whole week there several years ago and had a great time. I did not think it was too long. Here is my trip report with link to photos . To get to the Budapest part you need to scroll down a little more than half way.

http://www.fodors.com/community/europe/isabels-summer-trip-photos---to-italy-vienna-and-budapest.cfm

What a wonderful thing for you and your mother to do! I would think Budapest a delightful destination for your week together - it is such a beautiful city, with such a variety of things to see and do (and eat !) You've already been given a lot of good advice. You might also want to check into options for a day trip or overnight or two in Eger - I haven't visited Eger yet, but thought I might have enjoyed it.

J, the owner of the apartment we rented recommended our driver, Alajos Pulai at Budapest Airport Taxi.

http://budapestairporttaxi.com/Welcome.html

Alajos is very nice, speaks perfect English, and his cars are spotless. We felt his prices were very fair. Alajos arranged for one of his drivers to transport us from the airport. He was on time, with a sign with our names on it. Alajos himself spent the day trip we took to Lake Balaton and the Communist Statue park (a laugh, if nothing else!) and transported us to the train station.

An extra added benefit with Alajos is that his lovely wife is a masseuse and we took advantage of that as well.

LOVED Budapest, was there for 5 days in September 2012. I found it very reasonably priced and lots of stuff to do. Restaurants were great, quite cheap, and I loved the ambiance. If you like lemonade, I recommend you try it at different cafes and restaurants... I'd read here how great it was and I probably tasted 7-8 different "house" lemonades and loved every one of them!

We didn't do day trips, after 5 days we moved on to Vienna (and did a day trip to Bratislava) but found that there was still lots to do in Budapest itself. You could probably spend a couple half days at the different baths... loved it there

We enjoyed 3 days there when 65, and could have done a week.
The hungarian word for plaza is TER, and there are a number of nice ones. One we enjoyed was Liszt Ter, which seemed like a boulevard lined with cafes. Very pleasant way to dine. It was walkable from Pest's 'downtown', maybe 1/2 mile or so.

There's an Ethnography museum across from the Parliament; beautiful building, somewhat similar, but smaller than, to Vienna's Kunsthistoriche Museum. Interesting folk clothing from past centuries, plus some photos of peasants from the 19th century (made us appreciate why our ancestors left Europe). Good for 2 hours.

Our hotel concierge suggested a place to eat the first night. An all-you-can-eat buffet. The mere thought of which made us blanch, reminiscent of Old World Buffet, etc. Could not have been further from the truth...great atmosphere, inclusive price, unlimited wine, attentive personnel, TASTY food (labelled in both Hungarian and English). That enabled us to know what we'd like to order in subsequent restaurants. It seemed to cater to upper-class Budapestians and visiting businessmen. I recommend it highly. Maybe a mile from 'downtown' Pest. They must be doing things right...in 2006 they had one location, now there are 3. http://www.trofeagrill.com/index_eng.php

Great choice! I've been to Budapest three times and would love to go back.

For my last trip, start here:
http://mytimetotravel.wordpress.com/2012/02/11/nesting-in-budapest/

It includes a link for the lovely apartment I stayed in. The owner has several others in Budapest. On that trip I visited a brand-new museum, the Zelnik István Southeast Asian Gold Museum, as well as taking an Art Nouveau walking tour.

My second trip is here:
http://www.fodors.com/community/europe/the-sore-foot-tour---budapest-austria-venice.cfm

On that trip I visited Godollo, by train, which would be more interesting to fans of baroque. My first trip I visited Szentendre, by train and boat, but thought it was way too touristy.

Don't miss an evening boat tour on the Danube. Any guidebook will give you a list of the main sights, but Budapest is also a good city for just wandering around.

THank you all - I am now very excited and hoping I can fit in all of these suggestions in only a week. We have booked a week at the end of June, and tickets to the Opera and Budapest Festival Orchestra. I we will be drafting our itinerary around those evenings - and your daytime suggestions. Can anyone tell me what the dress code is at either the Opera (we're going the evening of the premiere) or at the Bela Bartok Hall? In either case, is it more than a nice summer dress? LBloom - thank you for the driver recommendation, I will definitely try to contact and arrange with Alajos! Thank you - I love this group, you're all wonderfully generous with your time and knowledge!
Jill

BMK for my trip planning to Budapest and Prague in September. Great ideas!

After the Opera we enjoyed dinner at Belcanto restaurant next door.



Also, evening drinks at Spoon Café every night before going back to our hotel nearby.

http://www.spooncafe.hu/