Budapest for beginners. Pest.
The city itself is split by the Danube into two pieces - Buda and Pest.
The Buda part is largely mountainous terrain with hills, slopes, rocks and steep roads. It has numerous parks, green fields and is generally considered to be a residential area. I will talk about it in the second part of the story.
Pest part is as flat as a pancake. It is largely administrative, business and shopping part of the city. You can engage into big city prowling and comb the streets of Vth District flooded with myriads of glowing brand boutiques. You can embark on a hunt for a local tie or shoe shop secluded in the numerous alleys radiating from main shopping street – Vaci utca. You may chose to dine in a posh restaurant on Zrinyi Utca or grab some falafels near Astoria subway station on your way to the next destination, sip a fresh fruit cocktail on Petofi Sandor Street or have a nice scoop of spicy chocolate ice-cream near St. Istvan Basilica.
Upon recharging your mind and body you may undertake a trip to the Hero's Square which is an independent lot. I would recommend promenading Andrassy Street unless you are not much of a walker. If so, take a bus or subway to get to the square. It is full of top attractions, including museums, theater, ancient castle and a huge park.
The park occupies both sides from the Kos Karoly street and accommodates a system of warm ponds inhabited by ducks that will gladly nip on bread if you bring them some. In wintertime the biggest pond turns into magnificent ice skating rink. If you feel like swimming you should go straight to the most famous spot of the park - Szechenyi hot baths. If not, stroll around the Vajdahunyad castle, sit on laps of Anonymous or stretch yourself on a deckchair to get some rest near the pond.
Before the dusk comes, make sure that you get a seat on Pest embankment of the Danube. There are movable chairs scattered along the embankment specially for tourists. Get comfortable and prepare to watch a striking picture when the whole city is set aglow. This is the best wrap-around view of the city skyline, Buda, the Danube and city bridges that you will ever get.