If "direct access" means "as soon as you exit the route you are in the downtown", then here are California examples that come to mind, besides the I-40 Los Angeles one from earlier:
I-5: Los Angeles (requires I-10 or US 101 from the south, or Route 170/US 101 or Route 110 from the north, Redding (requires either Route 273, Route 299 or Route 44)
I-80: Oakland (requires I-880 or I-580), Sacramento due to the 1982 route changes (requires using US 50 (former I-80) from the west, or I-5/Route 99 from the east)
I-8: San Diego (requires using Route 163 or I-5 to get to downtown)
I-10: San Bernardino (requires I-215 to get to downtown)
I-15: San Diego (requires Route 163 or Route 94 to get to downtown), Riverside (requires I-215/former I-15 (former I-15E later on), Los Angeles (requires using Route 60 or I-10)
US 101: San Jose (requires I-280 from the south or Route 87 from the north to get to downtown)
I-205: San Francisco (requires I-580 and I-80 to get there), Stockton (requires I-5 to get there)
I-405: Sacramento (must take I-5 north), Santa Monica (requires I-10 to get there), Long Beach (requires I-710 to get downtown), San Diego (must take I-5 to get there)
I-805: Los Angeles (requires I-5 to get there)
I-710: Pasadena (LOL)
I-215: San Diego (must use I-15 to get there), Barstow (must use I-15 to get there)
I-238: Stockton (requires I-580, I-205, and I-5 to get there)
I-380: San Bruno (need to drive a mile or two on El Camino Real to get towards the downtown area, which is along San Mateo Avenue and not directly on El Camino itself)
I-580: Oakland (downtown requires using either I-880 or I-980)
I-680: San Jose (downtown requires continuing onto I-280), Sacramento (requires using I-80 for approximately 40 miles east then US 50)
I-880: San Francisco at north terminus (requires using I-80), San Jose (requires using Coleman Avenue into other city streets, or I-280), Santa Cruz (requires continuing on Route 17)
Route 1: Los Angeles (need to use I-10 to reach downtown), Monterey (need to reach via Fremont Street exit), San Francisco (need to use I-280 from the south or US 101 from the north to reach downtown)
Route 2: Los Angeles (need to use US 101 to reach downtown)
Route 4: Concord (need to use Route 242 to reach downtown)
Route 13: Hayward (requires I-580 to Route 238)
Route 14: Los Angeles (requires I-5 to Route 170/US 101 or Route 110), Palmdale (requires Route 138 eastbound), Lancaster (have to go east on Avenue J)
Route 17: San Jose (have to take I-280 to reach downtown)
Route 24: Oakland (have to continue onto I-980 west)
Route 26: Stockton (downtown reached via Route 4)
Route 33: Ventura (must take Main Street exit towards Business US 101 then go east)
Route 37: San Rafael (requires switching to US 101), Vallejo (requires Route 29 southbound), Sacramento (must switch to I-80)
Route 46: Bakersfield (must switch over to Route 99 southbound)
US 50: San Francisco (must switch to I-80 westbound in West Sacramento)
Route 55: Riverside (requires going onto Route 91 eastbound)
Route 58: Bakersfield (requires using Route 204)
Route 60: Los Angeles (requires I-10 west), Pomona (requires Route 71 north from westbound 60)
Route 65: Roseville (must take Galleria Boulevard exit then go west)
Route 68: Monterey (see note on Route 1)
Route 70: Chico (reached via Route 149 and Route 99), Sacramento (reached via Route 99)
Route 73: San Diego (reached via I-5), Long Beach (reached via I-405 and Route 22)
Route 85: Gilroy (reached via US 101 south), Santa Cruz (reached via Route 17 south), Mountain View (downtown accessed by Evelyn Avenue), San Francisco (reached via US 101)
Route 87: San Francisco (reached via US 101)
Route 88: Stockton (downtown reached via Route 99 and Route 4)
Route 91: Los Angeles (requires going onto I-5 north to US 101 north, from Anaheim)
Route 92: San Mateo (downtown accessed via Route 82/El Camino Real), Stockton (reached via I-880, I-238, I-580, I-205 and I-5)
Route 99: Bakersfield (requires Route 178), Stockton (requires going west on Route 4), Lodi (requires using Lockeford Street west of business 99), Yuba City (requires Route 20), Chico (must go west on Route 32)
Route 113: Davis (downtown accessed via I-80 or via a mile drive along Covell Boulevard/former US 40/99W)
Route 116: Petaluma (downtown reached via the old highway routing along Lakeville into town, past current US 101)
Route 118: Ventura (downtown accessed via Route 126)
Route 120: San Francisco (accessed via I-5, I-205, I-580 and I-80)
Route 134: Ventura (accessed via US 101 north)
Route 138: Lancaster (see note on Route 14)
Route 149: Oroville and Marysville (both require using Route 70 to access), Chico and Red Bluff (requires Route 99 to access)
Route 152: San Jose (requires US 101 to get there)
Route 156: Monterey (requires Route 1 to get there), Los Banos (requires Route 152 to get there)
Route 163: Escondido (requires I-15 to get there)
Route 170: Hollywood (requires continuing on US 101 to get there), Sacramento (requires I-5 to get there)
Route 237: Oakland (requires I-880 to get there)
Route 241: Riverside (requires Route 91 to get there)
Route 242: Oakland (requires I-680 and Route 24 to get there - note that 242 is former Route 24)