Just thought id post a brief trip report as a first time visitor which might help other Buda newbies. I cant vouch for accuracy so only a guide.
We had a 4 night stay in BP recently.
Budapest airport is very modern and well organised. Its almost a pleasure to be in the place to arrive or depart. There is free wi fi and plenty of good quality shops and places to eat. On arrival,you may encounter people in the foyer offering taxi's etc.
If you go straight outside you will find the Fotaxi booth. Tell the attendant where you want to go and she will issue you with a fixed fare voucher and a contact card. You then get in the official Fotaxi cab and give the voucher to the driver. For example the fixed fare to the city centre chain bridge area was 5800ft. When you arrive, retain the voucher for your return journey.
To book your return journey to can pre book it on the Fotaxi website or swimply phone them and they will arrive quickly. Again show the driver the voucher and pay the fixed fare.
General safety-no issues encountered. Seems very safe by day and night. You may see homeless people in doorways and the odd drunk. also we noticed some prostitues loitering near major hotels. One or two were quite persistant at pursuing lone males and trying to hook them. This was at night time though.
Metro system-an excellent way of getting around. Fast efficient and cheap. Tickets appear to be 320ft for a single journey. You can buy tickets from the attendant or put coins in a machine at the stations. Very important..you will see orange machines on stands. You must insert your ticket in machine to validate it. Ticket inspectors operate,.some real,some fake and some corrupt. If they try to fine you,refuse to pay them and say you will pay later. Get off asap and leave. Do not give anyone money.
Eating out-plenty of places,both local and chain restaurants. Can be confusing as there is the bill,the service and a tip..all of which may or may not be expected and can be interchageable ! Check menu before sitting down and check whats included. There are all you can eat type places otherwise known as Troefea's notably one on Kiraly St
Foreign exchange-rates that easily better UK rates can be found in the many exchanges in the main shopping areas.
Baths-A must do experience which can be confusing ! We visited Szechenyi baths in City park which is at the end of Andrassy Ut and close to Heros Square.
On entry you will see four pay cubicles. Go to any of them. You can hire either a locker (with communal changing area) or a private Cabin. A Cabin may be shared if you are a couple though they are quite small. You will be issued with an electronic wrist band. Pass through the turnstile by showing the wrist band to the sensor. To find your cabin,you will see electronic displays on the walls at intervals. Hold your wristband to the display sensor area and it will validate you and display the locker number. If you now go to your locker and hold wristband to cabin door sensor,it will miraculously open ! You can then change and enter the baths. You can hire towels (downstairs) they are 600 ft with 1000ft returnable deposit. You MUST retain the paper receipt you are given in order to reclaim your 1000ft deposit. There are also lockers downstairs.
You could always bring your own towel or borrow one from your hotel room.
The Basilica- free entry except you are expected to drop a minimum gift of 200ft per person in the collection box at entrance. The Holy relic hand of st Stephen is only on display at certain times,typically from around 1300 to 1600 or thereabouts so visit in the afternoon. Watch out for concerts in the Basilica which you may like to attend.
Some hotels are worth calling into to admire the architecture,notably Greshams Four seasons.
Buda Hill/Palace..can be reached via funicular at end of chain bridge. There are single and return tickets.
Alternatively you could make the up and/or down trip using the steps which are just round to the right of the tunnel which is to the right of the funicular. The steps are called Kiraly lepcso. If you are using these steps at night,be a little careful and dont travel them on your own just in case.
Buda Hill..a good spread of small restaurants/shops etc. Some have set menu lunches and dinners etc.
When walking up the hill from the funicular towards St Matthias Church,at the junction of Tarnok and Disz Ter, you will see a supermarket. there is a small coffee shop upstairs and also a vast selection of local and international wines at good supermarket prices.
By the way if you are flying from the UK and changing at Schipol for Budapest,then you are entering a Schengen agreement border and you must pass through another passport control point. If your ticket is booked straight through,then it is likely you will arrive at Schipol in the upstairs arrivals area. Simply follow directions to your gate number and this will ensure you go the right way. Do not get confused and go downstairs>outside as you will then have entered Amsterdam and will then have to re-enter,pass security and this will delay you !
Hope this helps..