My son's 1st birthday was family and friends. We invited a bunch of his friends from a playgroup that were apart of. If you go to Safeway, I know for a fact that they will give you a free first birthday cake. Do not order anything with red icing/frosting on it. If it gets in the baby's eyes, it will cause problems. Or if you want to try something less sweet, try banana or apple muffins. Just stick a candle on top, dress up your son, get some cheap decor at the Dollar Store or 99 cent store. If you want to serve food for family/friends, ask if they can potluck or just serve muffins/cupcakes/cake and drinks.
For my son's 2nd birthday, we rented a bounce house and inflatable slide (that was when the backyard was just grass.
Now for my son's 3rd birthday, we went low-key since must husband got laid off, and just had a mini-bounce house, playground set in the backyard, and let the kids sing songs and dance in circles, paint with water and stencils, draw chalk on the concrete, and do some foam crafts. Plus the goodie bag I made was for "preschool theme". I included a fat piece of chalk, two foam sheets with stickers, a crayon, coloring page or two, a toy (random stuff collected from fast food restaurants or little party like toys you can find anywhere), box of raisins and bag of Mott's Real Applesauce Fruit Snacks. They loved it..no major junk food like candy, gum, etc.
But for my son's 4th birthday (he's a Dec baby so it's hard and this time I think we'll do it like the 2nd week of Nov). But we might step it up and do Way 2 Play Cafe.
There are tons of places in the area like parks (but you have to reserve a ramada), even the gyms such as gymboree, little gym, and other fun play places are expensive. Since you're son is only one go simple.
Good Luck!