JBD, if we're diving deeper than usual or longer than usual, we look at our air consumtion and bring out the calculators. Knowing your consumption rate is extremely important in order to calculate bottom times and deco times, and therefore the amount of gas needed for the dive. For simple recreational dives or very basic deco dives, we don't pay much attention to anything except air presure and our location underwater.
Up here, other factors often play into the equation for us such as getting cold. It's not often important to me to stay on a wreck for 90 minutes at 180' since I live a relatively short distance from where I dive. Besides that, it's pretty friggin' cold down there. Also, I don't like hanging forever so we often let our comfortable decompression time tell us how long a bottom time we'll have. More often than not, we just use the exact same plans that we have used in the past and you just get familiar with them. Again it all depends on the dive objective.
NINman, I think I understand your dilemma. You have a computer, but you don't want to rely on it, right? OK, if you're staying recreational, it's pretty simple. Take a water proof watch and a slate with you with a list of depths and their NDLs. Go to any depth you feel comfortable with and use the slate for back up. This will would work for the first dive, but repetitive dives get tricky if you 'puter chokes.
To really get out of the whole mess, you should learn the guts of decompression diving, and you can bail yourself out if your computer dies. For the type of diving you are talking about, there's nothing to be really worried about if you computer dies underwater -- just ascend slowly(30FPM), do a 5min safety stop, and always go slow from the safety stop to the surface. If the computer dies sometime during your trip, then you have no choice but to use tables (unless you're comfortable sharing a buddies 'puter). We use computer generated tables for our stuff.
Mike