When my oldest was an only child (age 0-3) I did spend more one on one time with him, but my suggestion even now with 2 children that entertain each other (now ages 5 and 2), it's still basically the same. I lived in a place that had A LOT to offer as far as opportunities for moms with kids before. The day was basically our morning routine (up early, stretch, prayer/meditation/shower, fix everyone breakfast, pack husband's lunch, etc, etc). Then I had some morning chores and I would just include him and turn them into games. Gathering/sorting laundry would be throwing laundry in the baskets like basketball, or showing him to sort "whites with whites, colors with colors, pants with pants", or when I'd sweep it rocked his world to hold the dustpan OR I'd let him swiffer and he loved that. From the time he was 2 he was able to go get the little trashbags out of the wastebaskets under the desk, by the beds, in the bathrooms and bring them to me, and I'd take the trash out. Silly little things like that, talking the whole time. It makes the chores take longer, but it's getting things done, teaching him, and playing at the same time. Then we'd play, read, sing, etc. Instead of chopping vegetables and stuff on the counter, sometimes I'd bring it all to the table and he'd sit in his chair and have a snack and watch and we'd talk about random stuff, practice something he was learning, or discuss cooking and what I was doing: he could tell you about "the trinity" (bellpeppers, garlic, onion) and what goes with what by about 2. When things are chopped I let him put stuff in the mixing bowls and have a go, or if mixing things, he could "squish" it and then I get a turn. Again it takes a little longer, but he was interested and it worked. We bonded over stuff I had to do anyway. Once it got to the part where you have to start cooking or broiling, you can just give him a couple wooden spoons, different sized pots and pans, and show him how different sizes make different sounds, and let him have at it. It helps keep him out from under foot, and it's sort of like an alarm in that if the drumming stops, you know to look for him, but otherwise you're free to cook without worry.
Going out: every day we would go for a walk. I still do this for my 2 year old-we pick one color, one shape for the week and practice it everywhere. Walk around looking for blue or squares, yellow and octagons, etc. Let your child inspect things (which means you're not going to be getting any aerobic exercise here----you may be watching ants march in a line or looking at broken chunks of concrete that your child is sure is a fossil, etc). You have a choice here to get aggravated that you're not going anywhere, or you can stop and watch knowledge, curiosity, imagination, and personality develop right before your very eyes. Was I perfect at that? Not on days when I'm at the store and rushing through, no.....but on my boys' outings, well, the outings are for them. We would walk down and feed stale bread or crackers to the turtles and ducks (and fish) at a nearby pond, play on the playground, go to the library for storytime and a craft or hear a special guest (our library has people do neat things like a drum circle, a childrens song guy with a banjo, Mad Science, the Critter Guy, etc), pick up 7 books and a movie or 2 for the week and go to the library every week. Now you have a book a day to read. We used to go to Small Fry Club at a local McDonalds for stories, games, crafts, guest speakers like a fireman, dentist, Ronald, etc (but we moved and this local McDonalds doesn't have that here). We'd look in our area and do whatever is available, whenever: children's theater to see a play, or a morning trip to the movie theater, swimming, zoo, art or sculpture musuems, (actually ANY museum), swimming, playdates, Bible study and letting your child play with peers at church, musical games, farmers market (let them ask questions and pick out one new thing a week to try in a dinner that evening). Tour a working farm, take lessons or classes together. Do different types of art projects together. Nap when your child naps, OR use that to get some chores/cooking done, or just veg out and play on the computer or read. If the weather is bad and there's no going outside, we can go to Chuck E Cheese, or walk the mall and ride the little carousel, "etc". If it's just my kids and I'm not babysitting, I'll let them put on their little boots and jackets and go splash around in the backyard on rainy days (for mild rains).
Right now: my guys have done some chores and a little preschool stuff with me. Now they're in the playroom upstairs. I'm just waiting on my neighbor's child to come over (any minute), since I provide childcare for her a few days a week. We'll do more playing, reading, preschool, and they can play together too. I am involved, but I also make sure to allow some "me time" where they're free to be kids and use their own imaginations too.