It's the thought that counts, not the cost. If a gift has been carefully chosen with me in mind and then beautifully wrapped it's always well-received by me.
Many people, especially the elderly, appreciate home-cooked treats - pickles, preserves, cookies, cakes etc. You could buy a cheap wicker basket and make up a selection. If you can't cook, choose speciality items from a budget price supermarket - a selection of cheeses, biscuits, a miniature bottle of wine or champagne, and a few chocolates.