I would chose public transport (if your luggage allows) and take the
X9 express bus towards
"Zoologischer Garten" (yes, this bus goes to the Western part of Berlin).
You have to get off this bus one stop before its terminal destination, i.e.
"Ernst-Reuter-Platz". When leaving the bus, you will find the underground
U2 right there. Get down the stairs and take the U2 towards "Pankow". Get off at "Stadtmitte". When you leave the underground towards "
Gendarmenmarkt" (i.e. the same direction as the train continues) and even take the second exit, you will be very near to the Hilton Berlin hotel entrance.
This would involve changing from bus X9 to underground U2 once, to overcome (not too long) stairs once down, once up. But compared to the bus TXL this will save you some walking and if the weather is bad, you will hardly be exposed to it, because the interchange at "Ernst-Reuter-Platz" is very convenient and so is exiting the U2 at "Stadtmitte".
This is my frequently practiced favourite way to get to the Hilton Berlin from the airport Tegel. I buy the corresponding ticket (one way, 24hrs ticket or 7days ticket, depending on my plans for using public transport in Berlin, fares can be found on the website
www.bvg.de) at the airport counter or the vending machine there. - However, a taxi would be an alternative, if you are unsure or in need of a more comfortable transport alternative.