I was fortunate enough to be able to combine a business trip with some holiday, and by chance, the Kempinski was the only hotel with room when I wanted to go.
I book a deal called a taste of the Danube that gave bed, breakfast, and each evening a plate of snacks and a glass of wine.
The hotel is well located in the centre, and has the advantage of being adjacent to the only metro station where the lines cross. Many of the tourist destinations are within walking distance, and the main shopping drag is just around the corner. Basically the location is excellent.
The hotel is modern and could be in any city - it lacks Hungarianess, and the main language is English. This is a good thing or a bad thing, depending on what you want. After a day of touring/work/eastern Europe , escaping to modern comfort is no bad thing. Rooms are large (I think I got an upgrade), comfortable, have most things needed for work/leisure, and there is usually a chocolate or something waiting for you on your return. The beds are very comfortable and use the very best linen that really makes you feel special.
I used the hotel chauffeured cars, and based on the stories of hassle that still exists if you use a taxi from the airport, this little expense for an executive limo was well worth it, because Budapest is still a little threatening, and the way the taxi drivers still dress in their leather jackets with mandatory hanging cigarette can be a little offputting. I was able to organise this by email before arrival, and it was just added on to my bill.

I only ate breakfast at the hotel, and it was amongst the best in Europe for variety and quality. Eating at the Hotel can be expensive, and there are so many good places in easy reach in the city, especially if you have a metro pass, that it is not an issue. The famous tea rooms whose name escapes me for the minute are just around the corner. Gundels is a short ride away, and despite what other reviews say, I found this no more expensive than eating out in Suburban London, and the quality, variety and experience were excellent. I thought Gundels Restaurant was a first rate experience
The hotel offers free wifi in the lobby, but you have to pay if you use internet in your room There is a concierge to help with trips, taxis and so on.
My problem now is that if I go back to Budapest, I will find it difficult to stay anywhere else. I now rate hotels against the Budapest Kempinski.
BTW, it was Gerbauds.