First a link to ZTM (public transport company in Warsaw).
This page shows all public transport lines. If you click on a number, it'll show you all the stops and if you click on a stop, it'll show you the timetable for that particular stop.
I am very impressed and it has been a very useful tool for me.
http://www.ztm.waw.pl/rozklad_nowy.php?c=182&l=2
Radom:
100 km from Warsaw.
KM train from Warsaw Srodm, 2:30 hours.
Very frequent Polski Busses, 1:40.
Host to the bi-annual Radom air show in August
Lublin:
I have always wanted to go to Lublin, so I checked this out as well.
TLK/IC trains from Warszawa Centralna, 2:30 hours.
The trains also stops in Warszawa Wschodnia station which makes the
trip 10-20 minutes faster and this station is more convenient coming
from the Doubletree hotel.
Pultusk:
Very frequent busses from Warszawa Zachodnia Bus station, 1 1/2
hours.
So it is certainly possible to do day trips to either of these cities/towns.
It is a little too much transport time for me personally, I would prefer to stay a night there.
So this time I probably won't be going to either place.
For my next visit to Warsaw I can plan accordingly.
For those of you familiar with Isaac Bashevis Singer: he lived in Ul. Krochmalna 10+12 for most of his childhood.