We spent a lot more of our time in Budapest on the Pest side of the river. The dominant landmark in Pest is the Hungarian parliament. This building was based on the British parliament in London as might be obvious if you compare the two.
Pest seems to be in general the better side of the river for wandering about aimlessly. While we just found a lot more interesting neighborhoods, there are two quantifiable reasons to claim that. First is that Pest is extremely flat so if you do get lost you at least don't have to do it up and down a series of hills. Secondly, public transportation is much better on the Pest side so it's pretty hard to stray too far from a major trolley or subway line.
Across from the Gellert Hill is Pest's central market. We invariably visit the central market in every city we go to if they happen to have one. This one looks a lot more like a train station from the exterior. Inside there are three levels. The top level is mostly souvenirs, the ground level is meat and produce and there is a fish market down in the basement level along with a couple small grocery stores.
Meat markets are particularly exciting in Hungary as they've spent the better part of the last millennium inventing new and exciting variants of smoked meats. Just about any meat market or grocery in the country has a wide array of salami-like things hanging somewhere in the store.
There are also a few bakeries down on the ground level but the most exciting street food around is actually in one corner of the market upstairs. Most of the top level is an endless display of linens, t-shirts, small gift bags of paprika and so on. Along one side there are a couple of stand-up bars (including the cheapest beer we found in all of Hungary) and also some stands selling langos, pastas, meat dishes and pizzas. A langos is sort of a small fried pizza with no toppings. The toppings are ordered when you buy the langos and cover the spectrum from sweet to savory. If you're looking for a complete meal with wine or beer for just a couple dollars (or euros), this is the place to be.
Pest has several pedestrian areas. This is Vaci Utca which is the main shopping street just a block in from the river. Several other pedestrian -only streets radiate out from here. During the day this is one of the livelier spots in Budapest. In the evening it quiets down. Our favorite area in the evening was the Franz Liszt Ter (Square) which is off of Andrassy Avenue near Oktagon. This square is basically a solid mass of restaurants with indoor and outdoor seating.
The St. Istvan basilica sits at the center of another pedestrian area. There aren't as many restaurants in this neighborhood but plenty of cafes and bars. Hungarians appear to be willing to drink coffee at any time of day for any reason whatsoever. We can't really comment on the coffee since neither of us tends to drink it but we can note that both Hungarian beers and Hungarian wines are eminently drinkable.
On a quiet street in central Pest, behind a large synagogue sits the metal weeping willow holocaust memorial. The leaves are inscribed with the names of the more than 500,000 Hungarian Jews who were murdered.
At the far end of Andrassy Avenue, well away from the river areas of Pest is Hősök tere which translates as heroes' square. Behind it in this view lies city park. When the colonnade was originally built the pedestals were intended for important members of the Habsburg dynasty which were ruling Austria-Hungary at the time. Now the statues in the colonnades represent important figures from Hungarian history and the statues around the base of the column represent the leaders of the Magyar tribes which founded Hungary.
Budapest's city park (varosliget) contains a couple museums, a zoo, a circus, a castle of sorts, a small amusement park, a duck pond and restaurant and the Szechenyi Baths. It's worth a visit even if you aren't coming to the baths but the baths (main entrance shown here) are an attraction by themselves. There are plenty of baths in Budapest, Szechenyi is a little friendlier to foreigners in that there is a small amount of signage in English. More than that you can rent a 'cabin' to change in. Cabins are not gender-specific so if you're with someone of the opposite sex and have hopes of actually finding them again somewhere on the other side of the changing rooms, Szechenyi is a good choice. It works sort of like this: In the main entrance hall you buy entrance passes and rent a cabin. This is sort of the default status assumed by the cashiers so if you fail to say anything useful in Hungarian, you'll still probably end up with it. Towels are not provided as part of this but you can rent them from the cabin attendant who seems to know the word for 'towel' in at least 20 different languages. We were led to our cabin where we changed and left our clothes inside. After changing, the attendant locks the cabin and gives you a tag with a number on it. It would be prudent to remember your number either way as you'll still have to find your way back to the cabin eventually.
Released from the changing rooms you are confronted with a long series of rooms. Every room contains one or more pools. The temperature of the water is posted somewhere nearby on a wall and in some cases the mineral make-up of the water as well. Along with maybe a dozen indoor pools there are at least 3 steam rooms (one of them at an unbelievable 60 degrees Celsius [140 F]) and maybe 4 or 5 saunas. Indoor pools range from 10 C (50 F) to 45 C (113 F). Some of the pools change seasonally so this could vary a bit. If you follow the string of pools far enough in one direction - you'll reach an actual exit to the outdoor pools in the courtyard of the baths. The outdoors pools look like this. There are three of them fully surrounded by the yellow palace-like structure of the building. These pools also vary in temperature and have an assortment of water features that turn on and off periodically including fountains, underwater jets and whirlpools. The cluster of people around the stairs in these pools are playing chess. There are other assorted treatments available at Szechenyi (the menu in the entrance hall is impressive) but we didn't partake of any of them. The baths alone were enough to amuse us for more than three hours.