My question is what will the surface temperature of the SS container be if not insulated (i.e. -300F?) and the LN2 is filled.
How accurately do you need this? Generally, the thermal conductivity of stainless is so high in comparison to the thermal convective heat transfer, that the steel is generally considered at liquid temperature. That's not true of course. To do this properly you need to consider the convective heat transfer between LN2 and stainless, the thermal conductive heat transfer across the stainless surface and then the convective heat transfer from the surface to atmosphere just as IRstuff mentions.
This analysis can be shortened a bit by assuming the convective heat transfer between the boiling LN2 and stainless wall is infinitely high (ie: no dT). You can then base the convective heat transfer of air on a shortcut provided in "Cryogenic Systems" by Randall Barron. For this, he gives a typical value of 0.25 Btu/ft2-s for LN2, LO2, LAr. This assumes relativly still air. For the thermal conductivity of stainless, I'd suggest checking with NIST, here:
Note at LN2 temp, thermal conductivity is roughly cut in half.
What kind of welding is needed to make sure the cold stress doesn't cause leak?
Generally, welding is not considered a problem area. Thermal contraction of the steel may produce stresses, but it's very hard to say much without a drawing. In general, a conventional tank that just sits on the ground will not be adversely affected in any way by the temperature. 304 is ductile even at this temperature, so there's much less of a problem than with other steels. You've got the best steel available for this application.
Will there be condensation inside the container?
A little bit inside, mostly outside. The outside of the container will be covered with frost, and that frost can build, creating a large ice ball around it. Note that as it does, it will change the thermal conductivity, and in general it adds a very poor layer of 'insulation'. If the vessel is completely open at the top, you'll get a little inside as frost falls off the cold portion of the tank above the LN2 and into the liquid. If there's a small opening in the top of your tank, or a back pressure regulator to maintain a blanket of nitrogen, that will provide a nitrogen blanket above the liquid and prevent any kind of condensation inside the tank.